1 /* 2 * OpenSimplex (Simplectic) Noise in Java. 3 * by Kurt Spencer 4 * 5 * v1.1 (October 5, 2014) 6 * - Added 2D and 4D implementations. 7 * - Proper gradient sets for all dimensions, from a 8 * dimensionally-generalizable scheme with an actual 9 * rhyme and reason behind it. 10 * - Removed default permutation array in favor of 11 * default seed. 12 * - Changed seed-based constructor to be independent 13 * of any particular randomization library, so results 14 * will be the same when ported to other languages. 15 */ 16 17 /** 18 * Ported to D by Brian Schott 19 */ 20 21 module opensimplexnoise; 22 import std.traits; 23 24 public class OpenSimplexNoise(T) if (isFloatingPoint!T) { 25 26 enum T STRETCH_CONSTANT_2D = -0.211324865405187; //(1/Math.sqrt(2+1)-1)/2; 27 enum T SQUISH_CONSTANT_2D = 0.366025403784439; //(Math.sqrt(2+1)-1)/2; 28 enum T STRETCH_CONSTANT_3D = -1.0 / 6; //(1/Math.sqrt(3+1)-1)/3; 29 enum T SQUISH_CONSTANT_3D = 1.0 / 3; //(Math.sqrt(3+1)-1)/3; 30 enum T STRETCH_CONSTANT_4D = -0.138196601125011; //(1/Math.sqrt(4+1)-1)/4; 31 enum T SQUISH_CONSTANT_4D = 0.309016994374947; //(Math.sqrt(4+1)-1)/4; 32 33 enum T NORM_CONSTANT_2D = 47; 34 enum T NORM_CONSTANT_3D = 103; 35 enum T NORM_CONSTANT_4D = 30; 36 37 enum long DEFAULT_SEED = 0; 38 39 private short[] perm; 40 private short[] permGradIndex3D; 41 42 public this() { 43 this(DEFAULT_SEED); 44 } 45 46 public this(short[] perm) { 47 this.perm = perm; 48 permGradIndex3D = new short[256]; 49 50 for (int i = 0; i < 256; i++) { 51 //Since 3D has 24 gradients, simple bitmask won't work, so precompute modulo array. 52 permGradIndex3D[i] = cast(short)((perm[i] % (gradients3D.length / 3)) * 3); 53 } 54 } 55 56 //Initializes the class using a permutation array generated from a 64-bit seed. 57 //Generates a proper permutation (i.e. doesn't merely perform N successive pair swaps on a base array) 58 //Uses a simple 64-bit LCG. 59 public this(long seed) { 60 perm = new short[256]; 61 permGradIndex3D = new short[256]; 62 short[] source = new short[256]; 63 for (short i = 0; i < 256; i++) 64 source[i] = i; 65 seed = seed * 6_364_136_223_846_793_005L + 1_442_695_040_888_963_407L; 66 seed = seed * 6_364_136_223_846_793_005L + 1_442_695_040_888_963_407L; 67 seed = seed * 6_364_136_223_846_793_005L + 1_442_695_040_888_963_407L; 68 for (int i = 255; i >= 0; i--) { 69 seed = seed * 6_364_136_223_846_793_005L + 1_442_695_040_888_963_407L; 70 int r = cast(int)((seed + 31) % (i + 1)); 71 if (r < 0) 72 r += (i + 1); 73 perm[i] = source[r]; 74 permGradIndex3D[i] = cast(short)((perm[i] % (gradients3D.length / 3)) * 3); 75 source[r] = source[i]; 76 } 77 } 78 79 //2D OpenSimplex (Simplectic) Noise. 80 public T eval(T x, T y) { 81 82 //Place input coordinates onto grid. 83 T stretchOffset = (x + y) * STRETCH_CONSTANT_2D; 84 T xs = x + stretchOffset; 85 T ys = y + stretchOffset; 86 87 //Floor to get grid coordinates of rhombus (stretched square) super-cell origin. 88 int xsb = fastFloor(xs); 89 int ysb = fastFloor(ys); 90 91 //Skew out to get actual coordinates of rhombus origin. We'll need these later. 92 T squishOffset = (xsb + ysb) * SQUISH_CONSTANT_2D; 93 T xb = xsb + squishOffset; 94 T yb = ysb + squishOffset; 95 96 //Compute grid coordinates relative to rhombus origin. 97 T xins = xs - xsb; 98 T yins = ys - ysb; 99 100 //Sum those together to get a value that determines which region we're in. 101 T inSum = xins + yins; 102 103 //Positions relative to origin point. 104 T dx0 = x - xb; 105 T dy0 = y - yb; 106 107 //We'll be defining these inside the next block and using them afterwards. 108 T dx_ext, dy_ext; 109 int xsv_ext, ysv_ext; 110 111 T value = 0; 112 113 //Contribution (1,0) 114 T dx1 = dx0 - 1 - SQUISH_CONSTANT_2D; 115 T dy1 = dy0 - 0 - SQUISH_CONSTANT_2D; 116 T attn1 = 2 - dx1 * dx1 - dy1 * dy1; 117 if (attn1 > 0) { 118 attn1 *= attn1; 119 value += attn1 * attn1 * extrapolate(xsb + 1, ysb + 0, dx1, dy1); 120 } 121 122 //Contribution (0,1) 123 T dx2 = dx0 - 0 - SQUISH_CONSTANT_2D; 124 T dy2 = dy0 - 1 - SQUISH_CONSTANT_2D; 125 T attn2 = 2 - dx2 * dx2 - dy2 * dy2; 126 if (attn2 > 0) { 127 attn2 *= attn2; 128 value += attn2 * attn2 * extrapolate(xsb + 0, ysb + 1, dx2, dy2); 129 } 130 131 if (inSum <= 1) { //We're inside the triangle (2-Simplex) at (0,0) 132 T zins = 1 - inSum; 133 if (zins > xins || zins > yins) { //(0,0) is one of the closest two triangular vertices 134 if (xins > yins) { 135 xsv_ext = xsb + 1; 136 ysv_ext = ysb - 1; 137 dx_ext = dx0 - 1; 138 dy_ext = dy0 + 1; 139 } else { 140 xsv_ext = xsb - 1; 141 ysv_ext = ysb + 1; 142 dx_ext = dx0 + 1; 143 dy_ext = dy0 - 1; 144 } 145 } else { //(1,0) and (0,1) are the closest two vertices. 146 xsv_ext = xsb + 1; 147 ysv_ext = ysb + 1; 148 dx_ext = dx0 - 1 - 2 * SQUISH_CONSTANT_2D; 149 dy_ext = dy0 - 1 - 2 * SQUISH_CONSTANT_2D; 150 } 151 } else { //We're inside the triangle (2-Simplex) at (1,1) 152 T zins = 2 - inSum; 153 if (zins < xins || zins < yins) { //(0,0) is one of the closest two triangular vertices 154 if (xins > yins) { 155 xsv_ext = xsb + 2; 156 ysv_ext = ysb + 0; 157 dx_ext = dx0 - 2 - 2 * SQUISH_CONSTANT_2D; 158 dy_ext = dy0 + 0 - 2 * SQUISH_CONSTANT_2D; 159 } else { 160 xsv_ext = xsb + 0; 161 ysv_ext = ysb + 2; 162 dx_ext = dx0 + 0 - 2 * SQUISH_CONSTANT_2D; 163 dy_ext = dy0 - 2 - 2 * SQUISH_CONSTANT_2D; 164 } 165 } else { //(1,0) and (0,1) are the closest two vertices. 166 dx_ext = dx0; 167 dy_ext = dy0; 168 xsv_ext = xsb; 169 ysv_ext = ysb; 170 } 171 xsb += 1; 172 ysb += 1; 173 dx0 = dx0 - 1 - 2 * SQUISH_CONSTANT_2D; 174 dy0 = dy0 - 1 - 2 * SQUISH_CONSTANT_2D; 175 } 176 177 //Contribution (0,0) or (1,1) 178 T attn0 = 2 - dx0 * dx0 - dy0 * dy0; 179 if (attn0 > 0) { 180 attn0 *= attn0; 181 value += attn0 * attn0 * extrapolate(xsb, ysb, dx0, dy0); 182 } 183 184 //Extra Vertex 185 T attn_ext = 2 - dx_ext * dx_ext - dy_ext * dy_ext; 186 if (attn_ext > 0) { 187 attn_ext *= attn_ext; 188 value += attn_ext * attn_ext * extrapolate(xsv_ext, ysv_ext, dx_ext, dy_ext); 189 } 190 191 return value / NORM_CONSTANT_2D; 192 } 193 194 //3D OpenSimplex (Simplectic) Noise. 195 public T eval(T x, T y, T z) { 196 197 //Place input coordinates on simplectic honeycomb. 198 T stretchOffset = (x + y + z) * STRETCH_CONSTANT_3D; 199 T xs = x + stretchOffset; 200 T ys = y + stretchOffset; 201 T zs = z + stretchOffset; 202 203 //Floor to get simplectic honeycomb coordinates of rhombohedron (stretched cube) super-cell origin. 204 int xsb = fastFloor(xs); 205 int ysb = fastFloor(ys); 206 int zsb = fastFloor(zs); 207 208 //Skew out to get actual coordinates of rhombohedron origin. We'll need these later. 209 T squishOffset = (xsb + ysb + zsb) * SQUISH_CONSTANT_3D; 210 T xb = xsb + squishOffset; 211 T yb = ysb + squishOffset; 212 T zb = zsb + squishOffset; 213 214 //Compute simplectic honeycomb coordinates relative to rhombohedral origin. 215 T xins = xs - xsb; 216 T yins = ys - ysb; 217 T zins = zs - zsb; 218 219 //Sum those together to get a value that determines which region we're in. 220 T inSum = xins + yins + zins; 221 222 //Positions relative to origin point. 223 T dx0 = x - xb; 224 T dy0 = y - yb; 225 T dz0 = z - zb; 226 227 //We'll be defining these inside the next block and using them afterwards. 228 T dx_ext0, dy_ext0, dz_ext0; 229 T dx_ext1, dy_ext1, dz_ext1; 230 int xsv_ext0, ysv_ext0, zsv_ext0; 231 int xsv_ext1, ysv_ext1, zsv_ext1; 232 233 T value = 0; 234 if (inSum <= 1) { //We're inside the tetrahedron (3-Simplex) at (0,0,0) 235 236 //Determine which two of (0,0,1), (0,1,0), (1,0,0) are closest. 237 byte aPoint = 0x01; 238 T aScore = xins; 239 byte bPoint = 0x02; 240 T bScore = yins; 241 if (aScore >= bScore && zins > bScore) { 242 bScore = zins; 243 bPoint = 0x04; 244 } else if (aScore < bScore && zins > aScore) { 245 aScore = zins; 246 aPoint = 0x04; 247 } 248 249 //Now we determine the two lattice points not part of the tetrahedron that may contribute. 250 //This depends on the closest two tetrahedral vertices, including (0,0,0) 251 T wins = 1 - inSum; 252 if (wins > aScore || wins > bScore) { //(0,0,0) is one of the closest two tetrahedral vertices. 253 byte c = (bScore > aScore ? bPoint : aPoint); //Our other closest vertex is the closest out of a and b. 254 255 if ((c & 0x01) == 0) { 256 xsv_ext0 = xsb - 1; 257 xsv_ext1 = xsb; 258 dx_ext0 = dx0 + 1; 259 dx_ext1 = dx0; 260 } else { 261 xsv_ext0 = xsv_ext1 = xsb + 1; 262 dx_ext0 = dx_ext1 = dx0 - 1; 263 } 264 265 if ((c & 0x02) == 0) { 266 ysv_ext0 = ysv_ext1 = ysb; 267 dy_ext0 = dy_ext1 = dy0; 268 if ((c & 0x01) == 0) { 269 ysv_ext1 -= 1; 270 dy_ext1 += 1; 271 } else { 272 ysv_ext0 -= 1; 273 dy_ext0 += 1; 274 } 275 } else { 276 ysv_ext0 = ysv_ext1 = ysb + 1; 277 dy_ext0 = dy_ext1 = dy0 - 1; 278 } 279 280 if ((c & 0x04) == 0) { 281 zsv_ext0 = zsb; 282 zsv_ext1 = zsb - 1; 283 dz_ext0 = dz0; 284 dz_ext1 = dz0 + 1; 285 } else { 286 zsv_ext0 = zsv_ext1 = zsb + 1; 287 dz_ext0 = dz_ext1 = dz0 - 1; 288 } 289 } else { //(0,0,0) is not one of the closest two tetrahedral vertices. 290 byte c = cast(byte)(aPoint | bPoint); //Our two extra vertices are determined by the closest two. 291 292 if ((c & 0x01) == 0) { 293 xsv_ext0 = xsb; 294 xsv_ext1 = xsb - 1; 295 dx_ext0 = dx0 - 2 * SQUISH_CONSTANT_3D; 296 dx_ext1 = dx0 + 1 - SQUISH_CONSTANT_3D; 297 } else { 298 xsv_ext0 = xsv_ext1 = xsb + 1; 299 dx_ext0 = dx0 - 1 - 2 * SQUISH_CONSTANT_3D; 300 dx_ext1 = dx0 - 1 - SQUISH_CONSTANT_3D; 301 } 302 303 if ((c & 0x02) == 0) { 304 ysv_ext0 = ysb; 305 ysv_ext1 = ysb - 1; 306 dy_ext0 = dy0 - 2 * SQUISH_CONSTANT_3D; 307 dy_ext1 = dy0 + 1 - SQUISH_CONSTANT_3D; 308 } else { 309 ysv_ext0 = ysv_ext1 = ysb + 1; 310 dy_ext0 = dy0 - 1 - 2 * SQUISH_CONSTANT_3D; 311 dy_ext1 = dy0 - 1 - SQUISH_CONSTANT_3D; 312 } 313 314 if ((c & 0x04) == 0) { 315 zsv_ext0 = zsb; 316 zsv_ext1 = zsb - 1; 317 dz_ext0 = dz0 - 2 * SQUISH_CONSTANT_3D; 318 dz_ext1 = dz0 + 1 - SQUISH_CONSTANT_3D; 319 } else { 320 zsv_ext0 = zsv_ext1 = zsb + 1; 321 dz_ext0 = dz0 - 1 - 2 * SQUISH_CONSTANT_3D; 322 dz_ext1 = dz0 - 1 - SQUISH_CONSTANT_3D; 323 } 324 } 325 326 //Contribution (0,0,0) 327 T attn0 = 2 - dx0 * dx0 - dy0 * dy0 - dz0 * dz0; 328 if (attn0 > 0) { 329 attn0 *= attn0; 330 value += attn0 * attn0 * extrapolate(xsb + 0, ysb + 0, zsb + 0, dx0, dy0, dz0); 331 } 332 333 //Contribution (1,0,0) 334 T dx1 = dx0 - 1 - SQUISH_CONSTANT_3D; 335 T dy1 = dy0 - 0 - SQUISH_CONSTANT_3D; 336 T dz1 = dz0 - 0 - SQUISH_CONSTANT_3D; 337 T attn1 = 2 - dx1 * dx1 - dy1 * dy1 - dz1 * dz1; 338 if (attn1 > 0) { 339 attn1 *= attn1; 340 value += attn1 * attn1 * extrapolate(xsb + 1, ysb + 0, zsb + 0, dx1, dy1, dz1); 341 } 342 343 //Contribution (0,1,0) 344 T dx2 = dx0 - 0 - SQUISH_CONSTANT_3D; 345 T dy2 = dy0 - 1 - SQUISH_CONSTANT_3D; 346 T dz2 = dz1; 347 T attn2 = 2 - dx2 * dx2 - dy2 * dy2 - dz2 * dz2; 348 if (attn2 > 0) { 349 attn2 *= attn2; 350 value += attn2 * attn2 * extrapolate(xsb + 0, ysb + 1, zsb + 0, dx2, dy2, dz2); 351 } 352 353 //Contribution (0,0,1) 354 T dx3 = dx2; 355 T dy3 = dy1; 356 T dz3 = dz0 - 1 - SQUISH_CONSTANT_3D; 357 T attn3 = 2 - dx3 * dx3 - dy3 * dy3 - dz3 * dz3; 358 if (attn3 > 0) { 359 attn3 *= attn3; 360 value += attn3 * attn3 * extrapolate(xsb + 0, ysb + 0, zsb + 1, dx3, dy3, dz3); 361 } 362 } else if (inSum >= 2) { //We're inside the tetrahedron (3-Simplex) at (1,1,1) 363 364 //Determine which two tetrahedral vertices are the closest, out of (1,1,0), (1,0,1), (0,1,1) but not (1,1,1). 365 byte aPoint = 0x06; 366 T aScore = xins; 367 byte bPoint = 0x05; 368 T bScore = yins; 369 if (aScore <= bScore && zins < bScore) { 370 bScore = zins; 371 bPoint = 0x03; 372 } else if (aScore > bScore && zins < aScore) { 373 aScore = zins; 374 aPoint = 0x03; 375 } 376 377 //Now we determine the two lattice points not part of the tetrahedron that may contribute. 378 //This depends on the closest two tetrahedral vertices, including (1,1,1) 379 T wins = 3 - inSum; 380 if (wins < aScore || wins < bScore) { //(1,1,1) is one of the closest two tetrahedral vertices. 381 byte c = (bScore < aScore ? bPoint : aPoint); //Our other closest vertex is the closest out of a and b. 382 383 if ((c & 0x01) != 0) { 384 xsv_ext0 = xsb + 2; 385 xsv_ext1 = xsb + 1; 386 dx_ext0 = dx0 - 2 - 3 * SQUISH_CONSTANT_3D; 387 dx_ext1 = dx0 - 1 - 3 * SQUISH_CONSTANT_3D; 388 } else { 389 xsv_ext0 = xsv_ext1 = xsb; 390 dx_ext0 = dx_ext1 = dx0 - 3 * SQUISH_CONSTANT_3D; 391 } 392 393 if ((c & 0x02) != 0) { 394 ysv_ext0 = ysv_ext1 = ysb + 1; 395 dy_ext0 = dy_ext1 = dy0 - 1 - 3 * SQUISH_CONSTANT_3D; 396 if ((c & 0x01) != 0) { 397 ysv_ext1 += 1; 398 dy_ext1 -= 1; 399 } else { 400 ysv_ext0 += 1; 401 dy_ext0 -= 1; 402 } 403 } else { 404 ysv_ext0 = ysv_ext1 = ysb; 405 dy_ext0 = dy_ext1 = dy0 - 3 * SQUISH_CONSTANT_3D; 406 } 407 408 if ((c & 0x04) != 0) { 409 zsv_ext0 = zsb + 1; 410 zsv_ext1 = zsb + 2; 411 dz_ext0 = dz0 - 1 - 3 * SQUISH_CONSTANT_3D; 412 dz_ext1 = dz0 - 2 - 3 * SQUISH_CONSTANT_3D; 413 } else { 414 zsv_ext0 = zsv_ext1 = zsb; 415 dz_ext0 = dz_ext1 = dz0 - 3 * SQUISH_CONSTANT_3D; 416 } 417 } else { //(1,1,1) is not one of the closest two tetrahedral vertices. 418 byte c = cast(byte)(aPoint & bPoint); //Our two extra vertices are determined by the closest two. 419 420 if ((c & 0x01) != 0) { 421 xsv_ext0 = xsb + 1; 422 xsv_ext1 = xsb + 2; 423 dx_ext0 = dx0 - 1 - SQUISH_CONSTANT_3D; 424 dx_ext1 = dx0 - 2 - 2 * SQUISH_CONSTANT_3D; 425 } else { 426 xsv_ext0 = xsv_ext1 = xsb; 427 dx_ext0 = dx0 - SQUISH_CONSTANT_3D; 428 dx_ext1 = dx0 - 2 * SQUISH_CONSTANT_3D; 429 } 430 431 if ((c & 0x02) != 0) { 432 ysv_ext0 = ysb + 1; 433 ysv_ext1 = ysb + 2; 434 dy_ext0 = dy0 - 1 - SQUISH_CONSTANT_3D; 435 dy_ext1 = dy0 - 2 - 2 * SQUISH_CONSTANT_3D; 436 } else { 437 ysv_ext0 = ysv_ext1 = ysb; 438 dy_ext0 = dy0 - SQUISH_CONSTANT_3D; 439 dy_ext1 = dy0 - 2 * SQUISH_CONSTANT_3D; 440 } 441 442 if ((c & 0x04) != 0) { 443 zsv_ext0 = zsb + 1; 444 zsv_ext1 = zsb + 2; 445 dz_ext0 = dz0 - 1 - SQUISH_CONSTANT_3D; 446 dz_ext1 = dz0 - 2 - 2 * SQUISH_CONSTANT_3D; 447 } else { 448 zsv_ext0 = zsv_ext1 = zsb; 449 dz_ext0 = dz0 - SQUISH_CONSTANT_3D; 450 dz_ext1 = dz0 - 2 * SQUISH_CONSTANT_3D; 451 } 452 } 453 454 //Contribution (1,1,0) 455 T dx3 = dx0 - 1 - 2 * SQUISH_CONSTANT_3D; 456 T dy3 = dy0 - 1 - 2 * SQUISH_CONSTANT_3D; 457 T dz3 = dz0 - 0 - 2 * SQUISH_CONSTANT_3D; 458 T attn3 = 2 - dx3 * dx3 - dy3 * dy3 - dz3 * dz3; 459 if (attn3 > 0) { 460 attn3 *= attn3; 461 value += attn3 * attn3 * extrapolate(xsb + 1, ysb + 1, zsb + 0, dx3, dy3, dz3); 462 } 463 464 //Contribution (1,0,1) 465 T dx2 = dx3; 466 T dy2 = dy0 - 0 - 2 * SQUISH_CONSTANT_3D; 467 T dz2 = dz0 - 1 - 2 * SQUISH_CONSTANT_3D; 468 T attn2 = 2 - dx2 * dx2 - dy2 * dy2 - dz2 * dz2; 469 if (attn2 > 0) { 470 attn2 *= attn2; 471 value += attn2 * attn2 * extrapolate(xsb + 1, ysb + 0, zsb + 1, dx2, dy2, dz2); 472 } 473 474 //Contribution (0,1,1) 475 T dx1 = dx0 - 0 - 2 * SQUISH_CONSTANT_3D; 476 T dy1 = dy3; 477 T dz1 = dz2; 478 T attn1 = 2 - dx1 * dx1 - dy1 * dy1 - dz1 * dz1; 479 if (attn1 > 0) { 480 attn1 *= attn1; 481 value += attn1 * attn1 * extrapolate(xsb + 0, ysb + 1, zsb + 1, dx1, dy1, dz1); 482 } 483 484 //Contribution (1,1,1) 485 dx0 = dx0 - 1 - 3 * SQUISH_CONSTANT_3D; 486 dy0 = dy0 - 1 - 3 * SQUISH_CONSTANT_3D; 487 dz0 = dz0 - 1 - 3 * SQUISH_CONSTANT_3D; 488 T attn0 = 2 - dx0 * dx0 - dy0 * dy0 - dz0 * dz0; 489 if (attn0 > 0) { 490 attn0 *= attn0; 491 value += attn0 * attn0 * extrapolate(xsb + 1, ysb + 1, zsb + 1, dx0, dy0, dz0); 492 } 493 } else { //We're inside the octahedron (Rectified 3-Simplex) in between. 494 T aScore; 495 byte aPoint; 496 bool aIsFurtherSide; 497 T bScore; 498 byte bPoint; 499 bool bIsFurtherSide; 500 501 //Decide between point (0,0,1) and (1,1,0) as closest 502 T p1 = xins + yins; 503 if (p1 > 1) { 504 aScore = p1 - 1; 505 aPoint = 0x03; 506 aIsFurtherSide = true; 507 } else { 508 aScore = 1 - p1; 509 aPoint = 0x04; 510 aIsFurtherSide = false; 511 } 512 513 //Decide between point (0,1,0) and (1,0,1) as closest 514 T p2 = xins + zins; 515 if (p2 > 1) { 516 bScore = p2 - 1; 517 bPoint = 0x05; 518 bIsFurtherSide = true; 519 } else { 520 bScore = 1 - p2; 521 bPoint = 0x02; 522 bIsFurtherSide = false; 523 } 524 525 //The closest out of the two (1,0,0) and (0,1,1) will replace the furthest out of the two decided above, if closer. 526 T p3 = yins + zins; 527 if (p3 > 1) { 528 T score = p3 - 1; 529 if (aScore <= bScore && aScore < score) { 530 aScore = score; 531 aPoint = 0x06; 532 aIsFurtherSide = true; 533 } else if (aScore > bScore && bScore < score) { 534 bScore = score; 535 bPoint = 0x06; 536 bIsFurtherSide = true; 537 } 538 } else { 539 T score = 1 - p3; 540 if (aScore <= bScore && aScore < score) { 541 aScore = score; 542 aPoint = 0x01; 543 aIsFurtherSide = false; 544 } else if (aScore > bScore && bScore < score) { 545 bScore = score; 546 bPoint = 0x01; 547 bIsFurtherSide = false; 548 } 549 } 550 551 //Where each of the two closest points are determines how the extra two vertices are calculated. 552 if (aIsFurtherSide == bIsFurtherSide) { 553 if (aIsFurtherSide) { //Both closest points on (1,1,1) side 554 555 //One of the two extra points is (1,1,1) 556 dx_ext0 = dx0 - 1 - 3 * SQUISH_CONSTANT_3D; 557 dy_ext0 = dy0 - 1 - 3 * SQUISH_CONSTANT_3D; 558 dz_ext0 = dz0 - 1 - 3 * SQUISH_CONSTANT_3D; 559 xsv_ext0 = xsb + 1; 560 ysv_ext0 = ysb + 1; 561 zsv_ext0 = zsb + 1; 562 563 //Other extra point is based on the shared axis. 564 byte c = cast(byte)(aPoint & bPoint); 565 if ((c & 0x01) != 0) { 566 dx_ext1 = dx0 - 2 - 2 * SQUISH_CONSTANT_3D; 567 dy_ext1 = dy0 - 2 * SQUISH_CONSTANT_3D; 568 dz_ext1 = dz0 - 2 * SQUISH_CONSTANT_3D; 569 xsv_ext1 = xsb + 2; 570 ysv_ext1 = ysb; 571 zsv_ext1 = zsb; 572 } else if ((c & 0x02) != 0) { 573 dx_ext1 = dx0 - 2 * SQUISH_CONSTANT_3D; 574 dy_ext1 = dy0 - 2 - 2 * SQUISH_CONSTANT_3D; 575 dz_ext1 = dz0 - 2 * SQUISH_CONSTANT_3D; 576 xsv_ext1 = xsb; 577 ysv_ext1 = ysb + 2; 578 zsv_ext1 = zsb; 579 } else { 580 dx_ext1 = dx0 - 2 * SQUISH_CONSTANT_3D; 581 dy_ext1 = dy0 - 2 * SQUISH_CONSTANT_3D; 582 dz_ext1 = dz0 - 2 - 2 * SQUISH_CONSTANT_3D; 583 xsv_ext1 = xsb; 584 ysv_ext1 = ysb; 585 zsv_ext1 = zsb + 2; 586 } 587 } else {//Both closest points on (0,0,0) side 588 589 //One of the two extra points is (0,0,0) 590 dx_ext0 = dx0; 591 dy_ext0 = dy0; 592 dz_ext0 = dz0; 593 xsv_ext0 = xsb; 594 ysv_ext0 = ysb; 595 zsv_ext0 = zsb; 596 597 //Other extra point is based on the omitted axis. 598 byte c = cast(byte)(aPoint | bPoint); 599 if ((c & 0x01) == 0) { 600 dx_ext1 = dx0 + 1 - SQUISH_CONSTANT_3D; 601 dy_ext1 = dy0 - 1 - SQUISH_CONSTANT_3D; 602 dz_ext1 = dz0 - 1 - SQUISH_CONSTANT_3D; 603 xsv_ext1 = xsb - 1; 604 ysv_ext1 = ysb + 1; 605 zsv_ext1 = zsb + 1; 606 } else if ((c & 0x02) == 0) { 607 dx_ext1 = dx0 - 1 - SQUISH_CONSTANT_3D; 608 dy_ext1 = dy0 + 1 - SQUISH_CONSTANT_3D; 609 dz_ext1 = dz0 - 1 - SQUISH_CONSTANT_3D; 610 xsv_ext1 = xsb + 1; 611 ysv_ext1 = ysb - 1; 612 zsv_ext1 = zsb + 1; 613 } else { 614 dx_ext1 = dx0 - 1 - SQUISH_CONSTANT_3D; 615 dy_ext1 = dy0 - 1 - SQUISH_CONSTANT_3D; 616 dz_ext1 = dz0 + 1 - SQUISH_CONSTANT_3D; 617 xsv_ext1 = xsb + 1; 618 ysv_ext1 = ysb + 1; 619 zsv_ext1 = zsb - 1; 620 } 621 } 622 } else { //One point on (0,0,0) side, one point on (1,1,1) side 623 byte c1, c2; 624 if (aIsFurtherSide) { 625 c1 = aPoint; 626 c2 = bPoint; 627 } else { 628 c1 = bPoint; 629 c2 = aPoint; 630 } 631 632 //One contribution is a permutation of (1,1,-1) 633 if ((c1 & 0x01) == 0) { 634 dx_ext0 = dx0 + 1 - SQUISH_CONSTANT_3D; 635 dy_ext0 = dy0 - 1 - SQUISH_CONSTANT_3D; 636 dz_ext0 = dz0 - 1 - SQUISH_CONSTANT_3D; 637 xsv_ext0 = xsb - 1; 638 ysv_ext0 = ysb + 1; 639 zsv_ext0 = zsb + 1; 640 } else if ((c1 & 0x02) == 0) { 641 dx_ext0 = dx0 - 1 - SQUISH_CONSTANT_3D; 642 dy_ext0 = dy0 + 1 - SQUISH_CONSTANT_3D; 643 dz_ext0 = dz0 - 1 - SQUISH_CONSTANT_3D; 644 xsv_ext0 = xsb + 1; 645 ysv_ext0 = ysb - 1; 646 zsv_ext0 = zsb + 1; 647 } else { 648 dx_ext0 = dx0 - 1 - SQUISH_CONSTANT_3D; 649 dy_ext0 = dy0 - 1 - SQUISH_CONSTANT_3D; 650 dz_ext0 = dz0 + 1 - SQUISH_CONSTANT_3D; 651 xsv_ext0 = xsb + 1; 652 ysv_ext0 = ysb + 1; 653 zsv_ext0 = zsb - 1; 654 } 655 656 //One contribution is a permutation of (0,0,2) 657 dx_ext1 = dx0 - 2 * SQUISH_CONSTANT_3D; 658 dy_ext1 = dy0 - 2 * SQUISH_CONSTANT_3D; 659 dz_ext1 = dz0 - 2 * SQUISH_CONSTANT_3D; 660 xsv_ext1 = xsb; 661 ysv_ext1 = ysb; 662 zsv_ext1 = zsb; 663 if ((c2 & 0x01) != 0) { 664 dx_ext1 -= 2; 665 xsv_ext1 += 2; 666 } else if ((c2 & 0x02) != 0) { 667 dy_ext1 -= 2; 668 ysv_ext1 += 2; 669 } else { 670 dz_ext1 -= 2; 671 zsv_ext1 += 2; 672 } 673 } 674 675 //Contribution (1,0,0) 676 T dx1 = dx0 - 1 - SQUISH_CONSTANT_3D; 677 T dy1 = dy0 - 0 - SQUISH_CONSTANT_3D; 678 T dz1 = dz0 - 0 - SQUISH_CONSTANT_3D; 679 T attn1 = 2 - dx1 * dx1 - dy1 * dy1 - dz1 * dz1; 680 if (attn1 > 0) { 681 attn1 *= attn1; 682 value += attn1 * attn1 * extrapolate(xsb + 1, ysb + 0, zsb + 0, dx1, dy1, dz1); 683 } 684 685 //Contribution (0,1,0) 686 T dx2 = dx0 - 0 - SQUISH_CONSTANT_3D; 687 T dy2 = dy0 - 1 - SQUISH_CONSTANT_3D; 688 T dz2 = dz1; 689 T attn2 = 2 - dx2 * dx2 - dy2 * dy2 - dz2 * dz2; 690 if (attn2 > 0) { 691 attn2 *= attn2; 692 value += attn2 * attn2 * extrapolate(xsb + 0, ysb + 1, zsb + 0, dx2, dy2, dz2); 693 } 694 695 //Contribution (0,0,1) 696 T dx3 = dx2; 697 T dy3 = dy1; 698 T dz3 = dz0 - 1 - SQUISH_CONSTANT_3D; 699 T attn3 = 2 - dx3 * dx3 - dy3 * dy3 - dz3 * dz3; 700 if (attn3 > 0) { 701 attn3 *= attn3; 702 value += attn3 * attn3 * extrapolate(xsb + 0, ysb + 0, zsb + 1, dx3, dy3, dz3); 703 } 704 705 //Contribution (1,1,0) 706 T dx4 = dx0 - 1 - 2 * SQUISH_CONSTANT_3D; 707 T dy4 = dy0 - 1 - 2 * SQUISH_CONSTANT_3D; 708 T dz4 = dz0 - 0 - 2 * SQUISH_CONSTANT_3D; 709 T attn4 = 2 - dx4 * dx4 - dy4 * dy4 - dz4 * dz4; 710 if (attn4 > 0) { 711 attn4 *= attn4; 712 value += attn4 * attn4 * extrapolate(xsb + 1, ysb + 1, zsb + 0, dx4, dy4, dz4); 713 } 714 715 //Contribution (1,0,1) 716 T dx5 = dx4; 717 T dy5 = dy0 - 0 - 2 * SQUISH_CONSTANT_3D; 718 T dz5 = dz0 - 1 - 2 * SQUISH_CONSTANT_3D; 719 T attn5 = 2 - dx5 * dx5 - dy5 * dy5 - dz5 * dz5; 720 if (attn5 > 0) { 721 attn5 *= attn5; 722 value += attn5 * attn5 * extrapolate(xsb + 1, ysb + 0, zsb + 1, dx5, dy5, dz5); 723 } 724 725 //Contribution (0,1,1) 726 T dx6 = dx0 - 0 - 2 * SQUISH_CONSTANT_3D; 727 T dy6 = dy4; 728 T dz6 = dz5; 729 T attn6 = 2 - dx6 * dx6 - dy6 * dy6 - dz6 * dz6; 730 if (attn6 > 0) { 731 attn6 *= attn6; 732 value += attn6 * attn6 * extrapolate(xsb + 0, ysb + 1, zsb + 1, dx6, dy6, dz6); 733 } 734 } 735 736 //First extra vertex 737 T attn_ext0 = 2 - dx_ext0 * dx_ext0 - dy_ext0 * dy_ext0 - dz_ext0 * dz_ext0; 738 if (attn_ext0 > 0) 739 { 740 attn_ext0 *= attn_ext0; 741 value += attn_ext0 * attn_ext0 * extrapolate(xsv_ext0, ysv_ext0, zsv_ext0, dx_ext0, dy_ext0, dz_ext0); 742 } 743 744 //Second extra vertex 745 T attn_ext1 = 2 - dx_ext1 * dx_ext1 - dy_ext1 * dy_ext1 - dz_ext1 * dz_ext1; 746 if (attn_ext1 > 0) 747 { 748 attn_ext1 *= attn_ext1; 749 value += attn_ext1 * attn_ext1 * extrapolate(xsv_ext1, ysv_ext1, zsv_ext1, dx_ext1, dy_ext1, dz_ext1); 750 } 751 752 return value / NORM_CONSTANT_3D; 753 } 754 755 //4D OpenSimplex (Simplectic) Noise. 756 public T eval(T x, T y, T z, T w) { 757 758 //Place input coordinates on simplectic honeycomb. 759 T stretchOffset = (x + y + z + w) * STRETCH_CONSTANT_4D; 760 T xs = x + stretchOffset; 761 T ys = y + stretchOffset; 762 T zs = z + stretchOffset; 763 T ws = w + stretchOffset; 764 765 //Floor to get simplectic honeycomb coordinates of rhombo-hypercube super-cell origin. 766 int xsb = fastFloor(xs); 767 int ysb = fastFloor(ys); 768 int zsb = fastFloor(zs); 769 int wsb = fastFloor(ws); 770 771 //Skew out to get actual coordinates of stretched rhombo-hypercube origin. We'll need these later. 772 T squishOffset = (xsb + ysb + zsb + wsb) * SQUISH_CONSTANT_4D; 773 T xb = xsb + squishOffset; 774 T yb = ysb + squishOffset; 775 T zb = zsb + squishOffset; 776 T wb = wsb + squishOffset; 777 778 //Compute simplectic honeycomb coordinates relative to rhombo-hypercube origin. 779 T xins = xs - xsb; 780 T yins = ys - ysb; 781 T zins = zs - zsb; 782 T wins = ws - wsb; 783 784 //Sum those together to get a value that determines which region we're in. 785 T inSum = xins + yins + zins + wins; 786 787 //Positions relative to origin point. 788 T dx0 = x - xb; 789 T dy0 = y - yb; 790 T dz0 = z - zb; 791 T dw0 = w - wb; 792 793 //We'll be defining these inside the next block and using them afterwards. 794 T dx_ext0, dy_ext0, dz_ext0, dw_ext0; 795 T dx_ext1, dy_ext1, dz_ext1, dw_ext1; 796 T dx_ext2, dy_ext2, dz_ext2, dw_ext2; 797 int xsv_ext0, ysv_ext0, zsv_ext0, wsv_ext0; 798 int xsv_ext1, ysv_ext1, zsv_ext1, wsv_ext1; 799 int xsv_ext2, ysv_ext2, zsv_ext2, wsv_ext2; 800 801 T value = 0; 802 if (inSum <= 1) { //We're inside the pentachoron (4-Simplex) at (0,0,0,0) 803 804 //Determine which two of (0,0,0,1), (0,0,1,0), (0,1,0,0), (1,0,0,0) are closest. 805 byte aPoint = 0x01; 806 T aScore = xins; 807 byte bPoint = 0x02; 808 T bScore = yins; 809 if (aScore >= bScore && zins > bScore) { 810 bScore = zins; 811 bPoint = 0x04; 812 } else if (aScore < bScore && zins > aScore) { 813 aScore = zins; 814 aPoint = 0x04; 815 } 816 if (aScore >= bScore && wins > bScore) { 817 bScore = wins; 818 bPoint = 0x08; 819 } else if (aScore < bScore && wins > aScore) { 820 aScore = wins; 821 aPoint = 0x08; 822 } 823 824 //Now we determine the three lattice points not part of the pentachoron that may contribute. 825 //This depends on the closest two pentachoron vertices, including (0,0,0,0) 826 T uins = 1 - inSum; 827 if (uins > aScore || uins > bScore) { //(0,0,0,0) is one of the closest two pentachoron vertices. 828 byte c = (bScore > aScore ? bPoint : aPoint); //Our other closest vertex is the closest out of a and b. 829 if ((c & 0x01) == 0) { 830 xsv_ext0 = xsb - 1; 831 xsv_ext1 = xsv_ext2 = xsb; 832 dx_ext0 = dx0 + 1; 833 dx_ext1 = dx_ext2 = dx0; 834 } else { 835 xsv_ext0 = xsv_ext1 = xsv_ext2 = xsb + 1; 836 dx_ext0 = dx_ext1 = dx_ext2 = dx0 - 1; 837 } 838 839 if ((c & 0x02) == 0) { 840 ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb; 841 dy_ext0 = dy_ext1 = dy_ext2 = dy0; 842 if ((c & 0x01) == 0x01) { 843 ysv_ext0 -= 1; 844 dy_ext0 += 1; 845 } else { 846 ysv_ext1 -= 1; 847 dy_ext1 += 1; 848 } 849 } else { 850 ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb + 1; 851 dy_ext0 = dy_ext1 = dy_ext2 = dy0 - 1; 852 } 853 854 if ((c & 0x04) == 0) { 855 zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb; 856 dz_ext0 = dz_ext1 = dz_ext2 = dz0; 857 if ((c & 0x03) != 0) { 858 if ((c & 0x03) == 0x03) { 859 zsv_ext0 -= 1; 860 dz_ext0 += 1; 861 } else { 862 zsv_ext1 -= 1; 863 dz_ext1 += 1; 864 } 865 } else { 866 zsv_ext2 -= 1; 867 dz_ext2 += 1; 868 } 869 } else { 870 zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb + 1; 871 dz_ext0 = dz_ext1 = dz_ext2 = dz0 - 1; 872 } 873 874 if ((c & 0x08) == 0) { 875 wsv_ext0 = wsv_ext1 = wsb; 876 wsv_ext2 = wsb - 1; 877 dw_ext0 = dw_ext1 = dw0; 878 dw_ext2 = dw0 + 1; 879 } else { 880 wsv_ext0 = wsv_ext1 = wsv_ext2 = wsb + 1; 881 dw_ext0 = dw_ext1 = dw_ext2 = dw0 - 1; 882 } 883 } else { //(0,0,0,0) is not one of the closest two pentachoron vertices. 884 byte c = cast(byte)(aPoint | bPoint); //Our three extra vertices are determined by the closest two. 885 886 if ((c & 0x01) == 0) { 887 xsv_ext0 = xsv_ext2 = xsb; 888 xsv_ext1 = xsb - 1; 889 dx_ext0 = dx0 - 2 * SQUISH_CONSTANT_4D; 890 dx_ext1 = dx0 + 1 - SQUISH_CONSTANT_4D; 891 dx_ext2 = dx0 - SQUISH_CONSTANT_4D; 892 } else { 893 xsv_ext0 = xsv_ext1 = xsv_ext2 = xsb + 1; 894 dx_ext0 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D; 895 dx_ext1 = dx_ext2 = dx0 - 1 - SQUISH_CONSTANT_4D; 896 } 897 898 if ((c & 0x02) == 0) { 899 ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb; 900 dy_ext0 = dy0 - 2 * SQUISH_CONSTANT_4D; 901 dy_ext1 = dy_ext2 = dy0 - SQUISH_CONSTANT_4D; 902 if ((c & 0x01) == 0x01) { 903 ysv_ext1 -= 1; 904 dy_ext1 += 1; 905 } else { 906 ysv_ext2 -= 1; 907 dy_ext2 += 1; 908 } 909 } else { 910 ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb + 1; 911 dy_ext0 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D; 912 dy_ext1 = dy_ext2 = dy0 - 1 - SQUISH_CONSTANT_4D; 913 } 914 915 if ((c & 0x04) == 0) { 916 zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb; 917 dz_ext0 = dz0 - 2 * SQUISH_CONSTANT_4D; 918 dz_ext1 = dz_ext2 = dz0 - SQUISH_CONSTANT_4D; 919 if ((c & 0x03) == 0x03) { 920 zsv_ext1 -= 1; 921 dz_ext1 += 1; 922 } else { 923 zsv_ext2 -= 1; 924 dz_ext2 += 1; 925 } 926 } else { 927 zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb + 1; 928 dz_ext0 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D; 929 dz_ext1 = dz_ext2 = dz0 - 1 - SQUISH_CONSTANT_4D; 930 } 931 932 if ((c & 0x08) == 0) { 933 wsv_ext0 = wsv_ext1 = wsb; 934 wsv_ext2 = wsb - 1; 935 dw_ext0 = dw0 - 2 * SQUISH_CONSTANT_4D; 936 dw_ext1 = dw0 - SQUISH_CONSTANT_4D; 937 dw_ext2 = dw0 + 1 - SQUISH_CONSTANT_4D; 938 } else { 939 wsv_ext0 = wsv_ext1 = wsv_ext2 = wsb + 1; 940 dw_ext0 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D; 941 dw_ext1 = dw_ext2 = dw0 - 1 - SQUISH_CONSTANT_4D; 942 } 943 } 944 945 //Contribution (0,0,0,0) 946 T attn0 = 2 - dx0 * dx0 - dy0 * dy0 - dz0 * dz0 - dw0 * dw0; 947 if (attn0 > 0) { 948 attn0 *= attn0; 949 value += attn0 * attn0 * extrapolate(xsb + 0, ysb + 0, zsb + 0, wsb + 0, dx0, dy0, dz0, dw0); 950 } 951 952 //Contribution (1,0,0,0) 953 T dx1 = dx0 - 1 - SQUISH_CONSTANT_4D; 954 T dy1 = dy0 - 0 - SQUISH_CONSTANT_4D; 955 T dz1 = dz0 - 0 - SQUISH_CONSTANT_4D; 956 T dw1 = dw0 - 0 - SQUISH_CONSTANT_4D; 957 T attn1 = 2 - dx1 * dx1 - dy1 * dy1 - dz1 * dz1 - dw1 * dw1; 958 if (attn1 > 0) { 959 attn1 *= attn1; 960 value += attn1 * attn1 * extrapolate(xsb + 1, ysb + 0, zsb + 0, wsb + 0, dx1, dy1, dz1, dw1); 961 } 962 963 //Contribution (0,1,0,0) 964 T dx2 = dx0 - 0 - SQUISH_CONSTANT_4D; 965 T dy2 = dy0 - 1 - SQUISH_CONSTANT_4D; 966 T dz2 = dz1; 967 T dw2 = dw1; 968 T attn2 = 2 - dx2 * dx2 - dy2 * dy2 - dz2 * dz2 - dw2 * dw2; 969 if (attn2 > 0) { 970 attn2 *= attn2; 971 value += attn2 * attn2 * extrapolate(xsb + 0, ysb + 1, zsb + 0, wsb + 0, dx2, dy2, dz2, dw2); 972 } 973 974 //Contribution (0,0,1,0) 975 T dx3 = dx2; 976 T dy3 = dy1; 977 T dz3 = dz0 - 1 - SQUISH_CONSTANT_4D; 978 T dw3 = dw1; 979 T attn3 = 2 - dx3 * dx3 - dy3 * dy3 - dz3 * dz3 - dw3 * dw3; 980 if (attn3 > 0) { 981 attn3 *= attn3; 982 value += attn3 * attn3 * extrapolate(xsb + 0, ysb + 0, zsb + 1, wsb + 0, dx3, dy3, dz3, dw3); 983 } 984 985 //Contribution (0,0,0,1) 986 T dx4 = dx2; 987 T dy4 = dy1; 988 T dz4 = dz1; 989 T dw4 = dw0 - 1 - SQUISH_CONSTANT_4D; 990 T attn4 = 2 - dx4 * dx4 - dy4 * dy4 - dz4 * dz4 - dw4 * dw4; 991 if (attn4 > 0) { 992 attn4 *= attn4; 993 value += attn4 * attn4 * extrapolate(xsb + 0, ysb + 0, zsb + 0, wsb + 1, dx4, dy4, dz4, dw4); 994 } 995 } else if (inSum >= 3) { //We're inside the pentachoron (4-Simplex) at (1,1,1,1) 996 //Determine which two of (1,1,1,0), (1,1,0,1), (1,0,1,1), (0,1,1,1) are closest. 997 byte aPoint = 0x0E; 998 T aScore = xins; 999 byte bPoint = 0x0D; 1000 T bScore = yins; 1001 if (aScore <= bScore && zins < bScore) { 1002 bScore = zins; 1003 bPoint = 0x0B; 1004 } else if (aScore > bScore && zins < aScore) { 1005 aScore = zins; 1006 aPoint = 0x0B; 1007 } 1008 if (aScore <= bScore && wins < bScore) { 1009 bScore = wins; 1010 bPoint = 0x07; 1011 } else if (aScore > bScore && wins < aScore) { 1012 aScore = wins; 1013 aPoint = 0x07; 1014 } 1015 1016 //Now we determine the three lattice points not part of the pentachoron that may contribute. 1017 //This depends on the closest two pentachoron vertices, including (0,0,0,0) 1018 T uins = 4 - inSum; 1019 if (uins < aScore || uins < bScore) { //(1,1,1,1) is one of the closest two pentachoron vertices. 1020 byte c = (bScore < aScore ? bPoint : aPoint); //Our other closest vertex is the closest out of a and b. 1021 1022 if ((c & 0x01) != 0) { 1023 xsv_ext0 = xsb + 2; 1024 xsv_ext1 = xsv_ext2 = xsb + 1; 1025 dx_ext0 = dx0 - 2 - 4 * SQUISH_CONSTANT_4D; 1026 dx_ext1 = dx_ext2 = dx0 - 1 - 4 * SQUISH_CONSTANT_4D; 1027 } else { 1028 xsv_ext0 = xsv_ext1 = xsv_ext2 = xsb; 1029 dx_ext0 = dx_ext1 = dx_ext2 = dx0 - 4 * SQUISH_CONSTANT_4D; 1030 } 1031 1032 if ((c & 0x02) != 0) { 1033 ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb + 1; 1034 dy_ext0 = dy_ext1 = dy_ext2 = dy0 - 1 - 4 * SQUISH_CONSTANT_4D; 1035 if ((c & 0x01) != 0) { 1036 ysv_ext1 += 1; 1037 dy_ext1 -= 1; 1038 } else { 1039 ysv_ext0 += 1; 1040 dy_ext0 -= 1; 1041 } 1042 } else { 1043 ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb; 1044 dy_ext0 = dy_ext1 = dy_ext2 = dy0 - 4 * SQUISH_CONSTANT_4D; 1045 } 1046 1047 if ((c & 0x04) != 0) { 1048 zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb + 1; 1049 dz_ext0 = dz_ext1 = dz_ext2 = dz0 - 1 - 4 * SQUISH_CONSTANT_4D; 1050 if ((c & 0x03) != 0x03) { 1051 if ((c & 0x03) == 0) { 1052 zsv_ext0 += 1; 1053 dz_ext0 -= 1; 1054 } else { 1055 zsv_ext1 += 1; 1056 dz_ext1 -= 1; 1057 } 1058 } else { 1059 zsv_ext2 += 1; 1060 dz_ext2 -= 1; 1061 } 1062 } else { 1063 zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb; 1064 dz_ext0 = dz_ext1 = dz_ext2 = dz0 - 4 * SQUISH_CONSTANT_4D; 1065 } 1066 1067 if ((c & 0x08) != 0) { 1068 wsv_ext0 = wsv_ext1 = wsb + 1; 1069 wsv_ext2 = wsb + 2; 1070 dw_ext0 = dw_ext1 = dw0 - 1 - 4 * SQUISH_CONSTANT_4D; 1071 dw_ext2 = dw0 - 2 - 4 * SQUISH_CONSTANT_4D; 1072 } else { 1073 wsv_ext0 = wsv_ext1 = wsv_ext2 = wsb; 1074 dw_ext0 = dw_ext1 = dw_ext2 = dw0 - 4 * SQUISH_CONSTANT_4D; 1075 } 1076 } else { //(1,1,1,1) is not one of the closest two pentachoron vertices. 1077 byte c = cast(byte)(aPoint & bPoint); //Our three extra vertices are determined by the closest two. 1078 1079 if ((c & 0x01) != 0) { 1080 xsv_ext0 = xsv_ext2 = xsb + 1; 1081 xsv_ext1 = xsb + 2; 1082 dx_ext0 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D; 1083 dx_ext1 = dx0 - 2 - 3 * SQUISH_CONSTANT_4D; 1084 dx_ext2 = dx0 - 1 - 3 * SQUISH_CONSTANT_4D; 1085 } else { 1086 xsv_ext0 = xsv_ext1 = xsv_ext2 = xsb; 1087 dx_ext0 = dx0 - 2 * SQUISH_CONSTANT_4D; 1088 dx_ext1 = dx_ext2 = dx0 - 3 * SQUISH_CONSTANT_4D; 1089 } 1090 1091 if ((c & 0x02) != 0) { 1092 ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb + 1; 1093 dy_ext0 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D; 1094 dy_ext1 = dy_ext2 = dy0 - 1 - 3 * SQUISH_CONSTANT_4D; 1095 if ((c & 0x01) != 0) { 1096 ysv_ext2 += 1; 1097 dy_ext2 -= 1; 1098 } else { 1099 ysv_ext1 += 1; 1100 dy_ext1 -= 1; 1101 } 1102 } else { 1103 ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb; 1104 dy_ext0 = dy0 - 2 * SQUISH_CONSTANT_4D; 1105 dy_ext1 = dy_ext2 = dy0 - 3 * SQUISH_CONSTANT_4D; 1106 } 1107 1108 if ((c & 0x04) != 0) { 1109 zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb + 1; 1110 dz_ext0 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D; 1111 dz_ext1 = dz_ext2 = dz0 - 1 - 3 * SQUISH_CONSTANT_4D; 1112 if ((c & 0x03) != 0) { 1113 zsv_ext2 += 1; 1114 dz_ext2 -= 1; 1115 } else { 1116 zsv_ext1 += 1; 1117 dz_ext1 -= 1; 1118 } 1119 } else { 1120 zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb; 1121 dz_ext0 = dz0 - 2 * SQUISH_CONSTANT_4D; 1122 dz_ext1 = dz_ext2 = dz0 - 3 * SQUISH_CONSTANT_4D; 1123 } 1124 1125 if ((c & 0x08) != 0) { 1126 wsv_ext0 = wsv_ext1 = wsb + 1; 1127 wsv_ext2 = wsb + 2; 1128 dw_ext0 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D; 1129 dw_ext1 = dw0 - 1 - 3 * SQUISH_CONSTANT_4D; 1130 dw_ext2 = dw0 - 2 - 3 * SQUISH_CONSTANT_4D; 1131 } else { 1132 wsv_ext0 = wsv_ext1 = wsv_ext2 = wsb; 1133 dw_ext0 = dw0 - 2 * SQUISH_CONSTANT_4D; 1134 dw_ext1 = dw_ext2 = dw0 - 3 * SQUISH_CONSTANT_4D; 1135 } 1136 } 1137 1138 //Contribution (1,1,1,0) 1139 T dx4 = dx0 - 1 - 3 * SQUISH_CONSTANT_4D; 1140 T dy4 = dy0 - 1 - 3 * SQUISH_CONSTANT_4D; 1141 T dz4 = dz0 - 1 - 3 * SQUISH_CONSTANT_4D; 1142 T dw4 = dw0 - 3 * SQUISH_CONSTANT_4D; 1143 T attn4 = 2 - dx4 * dx4 - dy4 * dy4 - dz4 * dz4 - dw4 * dw4; 1144 if (attn4 > 0) { 1145 attn4 *= attn4; 1146 value += attn4 * attn4 * extrapolate(xsb + 1, ysb + 1, zsb + 1, wsb + 0, dx4, dy4, dz4, dw4); 1147 } 1148 1149 //Contribution (1,1,0,1) 1150 T dx3 = dx4; 1151 T dy3 = dy4; 1152 T dz3 = dz0 - 3 * SQUISH_CONSTANT_4D; 1153 T dw3 = dw0 - 1 - 3 * SQUISH_CONSTANT_4D; 1154 T attn3 = 2 - dx3 * dx3 - dy3 * dy3 - dz3 * dz3 - dw3 * dw3; 1155 if (attn3 > 0) { 1156 attn3 *= attn3; 1157 value += attn3 * attn3 * extrapolate(xsb + 1, ysb + 1, zsb + 0, wsb + 1, dx3, dy3, dz3, dw3); 1158 } 1159 1160 //Contribution (1,0,1,1) 1161 T dx2 = dx4; 1162 T dy2 = dy0 - 3 * SQUISH_CONSTANT_4D; 1163 T dz2 = dz4; 1164 T dw2 = dw3; 1165 T attn2 = 2 - dx2 * dx2 - dy2 * dy2 - dz2 * dz2 - dw2 * dw2; 1166 if (attn2 > 0) { 1167 attn2 *= attn2; 1168 value += attn2 * attn2 * extrapolate(xsb + 1, ysb + 0, zsb + 1, wsb + 1, dx2, dy2, dz2, dw2); 1169 } 1170 1171 //Contribution (0,1,1,1) 1172 T dx1 = dx0 - 3 * SQUISH_CONSTANT_4D; 1173 T dz1 = dz4; 1174 T dy1 = dy4; 1175 T dw1 = dw3; 1176 T attn1 = 2 - dx1 * dx1 - dy1 * dy1 - dz1 * dz1 - dw1 * dw1; 1177 if (attn1 > 0) { 1178 attn1 *= attn1; 1179 value += attn1 * attn1 * extrapolate(xsb + 0, ysb + 1, zsb + 1, wsb + 1, dx1, dy1, dz1, dw1); 1180 } 1181 1182 //Contribution (1,1,1,1) 1183 dx0 = dx0 - 1 - 4 * SQUISH_CONSTANT_4D; 1184 dy0 = dy0 - 1 - 4 * SQUISH_CONSTANT_4D; 1185 dz0 = dz0 - 1 - 4 * SQUISH_CONSTANT_4D; 1186 dw0 = dw0 - 1 - 4 * SQUISH_CONSTANT_4D; 1187 T attn0 = 2 - dx0 * dx0 - dy0 * dy0 - dz0 * dz0 - dw0 * dw0; 1188 if (attn0 > 0) { 1189 attn0 *= attn0; 1190 value += attn0 * attn0 * extrapolate(xsb + 1, ysb + 1, zsb + 1, wsb + 1, dx0, dy0, dz0, dw0); 1191 } 1192 } else if (inSum <= 2) { //We're inside the first dispentachoron (Rectified 4-Simplex) 1193 T aScore; 1194 byte aPoint; 1195 bool aIsBiggerSide = true; 1196 T bScore; 1197 byte bPoint; 1198 bool bIsBiggerSide = true; 1199 1200 //Decide between (1,1,0,0) and (0,0,1,1) 1201 if (xins + yins > zins + wins) { 1202 aScore = xins + yins; 1203 aPoint = 0x03; 1204 } else { 1205 aScore = zins + wins; 1206 aPoint = 0x0C; 1207 } 1208 1209 //Decide between (1,0,1,0) and (0,1,0,1) 1210 if (xins + zins > yins + wins) { 1211 bScore = xins + zins; 1212 bPoint = 0x05; 1213 } else { 1214 bScore = yins + wins; 1215 bPoint = 0x0A; 1216 } 1217 1218 //Closer between (1,0,0,1) and (0,1,1,0) will replace the further of a and b, if closer. 1219 if (xins + wins > yins + zins) { 1220 T score = xins + wins; 1221 if (aScore >= bScore && score > bScore) { 1222 bScore = score; 1223 bPoint = 0x09; 1224 } else if (aScore < bScore && score > aScore) { 1225 aScore = score; 1226 aPoint = 0x09; 1227 } 1228 } else { 1229 T score = yins + zins; 1230 if (aScore >= bScore && score > bScore) { 1231 bScore = score; 1232 bPoint = 0x06; 1233 } else if (aScore < bScore && score > aScore) { 1234 aScore = score; 1235 aPoint = 0x06; 1236 } 1237 } 1238 1239 //Decide if (1,0,0,0) is closer. 1240 T p1 = 2 - inSum + xins; 1241 if (aScore >= bScore && p1 > bScore) { 1242 bScore = p1; 1243 bPoint = 0x01; 1244 bIsBiggerSide = false; 1245 } else if (aScore < bScore && p1 > aScore) { 1246 aScore = p1; 1247 aPoint = 0x01; 1248 aIsBiggerSide = false; 1249 } 1250 1251 //Decide if (0,1,0,0) is closer. 1252 T p2 = 2 - inSum + yins; 1253 if (aScore >= bScore && p2 > bScore) { 1254 bScore = p2; 1255 bPoint = 0x02; 1256 bIsBiggerSide = false; 1257 } else if (aScore < bScore && p2 > aScore) { 1258 aScore = p2; 1259 aPoint = 0x02; 1260 aIsBiggerSide = false; 1261 } 1262 1263 //Decide if (0,0,1,0) is closer. 1264 T p3 = 2 - inSum + zins; 1265 if (aScore >= bScore && p3 > bScore) { 1266 bScore = p3; 1267 bPoint = 0x04; 1268 bIsBiggerSide = false; 1269 } else if (aScore < bScore && p3 > aScore) { 1270 aScore = p3; 1271 aPoint = 0x04; 1272 aIsBiggerSide = false; 1273 } 1274 1275 //Decide if (0,0,0,1) is closer. 1276 T p4 = 2 - inSum + wins; 1277 if (aScore >= bScore && p4 > bScore) { 1278 bScore = p4; 1279 bPoint = 0x08; 1280 bIsBiggerSide = false; 1281 } else if (aScore < bScore && p4 > aScore) { 1282 aScore = p4; 1283 aPoint = 0x08; 1284 aIsBiggerSide = false; 1285 } 1286 1287 //Where each of the two closest points are determines how the extra three vertices are calculated. 1288 if (aIsBiggerSide == bIsBiggerSide) { 1289 if (aIsBiggerSide) { //Both closest points on the bigger side 1290 byte c1 = cast(byte)(aPoint | bPoint); 1291 byte c2 = cast(byte)(aPoint & bPoint); 1292 if ((c1 & 0x01) == 0) { 1293 xsv_ext0 = xsb; 1294 xsv_ext1 = xsb - 1; 1295 dx_ext0 = dx0 - 3 * SQUISH_CONSTANT_4D; 1296 dx_ext1 = dx0 + 1 - 2 * SQUISH_CONSTANT_4D; 1297 } else { 1298 xsv_ext0 = xsv_ext1 = xsb + 1; 1299 dx_ext0 = dx0 - 1 - 3 * SQUISH_CONSTANT_4D; 1300 dx_ext1 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D; 1301 } 1302 1303 if ((c1 & 0x02) == 0) { 1304 ysv_ext0 = ysb; 1305 ysv_ext1 = ysb - 1; 1306 dy_ext0 = dy0 - 3 * SQUISH_CONSTANT_4D; 1307 dy_ext1 = dy0 + 1 - 2 * SQUISH_CONSTANT_4D; 1308 } else { 1309 ysv_ext0 = ysv_ext1 = ysb + 1; 1310 dy_ext0 = dy0 - 1 - 3 * SQUISH_CONSTANT_4D; 1311 dy_ext1 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D; 1312 } 1313 1314 if ((c1 & 0x04) == 0) { 1315 zsv_ext0 = zsb; 1316 zsv_ext1 = zsb - 1; 1317 dz_ext0 = dz0 - 3 * SQUISH_CONSTANT_4D; 1318 dz_ext1 = dz0 + 1 - 2 * SQUISH_CONSTANT_4D; 1319 } else { 1320 zsv_ext0 = zsv_ext1 = zsb + 1; 1321 dz_ext0 = dz0 - 1 - 3 * SQUISH_CONSTANT_4D; 1322 dz_ext1 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D; 1323 } 1324 1325 if ((c1 & 0x08) == 0) { 1326 wsv_ext0 = wsb; 1327 wsv_ext1 = wsb - 1; 1328 dw_ext0 = dw0 - 3 * SQUISH_CONSTANT_4D; 1329 dw_ext1 = dw0 + 1 - 2 * SQUISH_CONSTANT_4D; 1330 } else { 1331 wsv_ext0 = wsv_ext1 = wsb + 1; 1332 dw_ext0 = dw0 - 1 - 3 * SQUISH_CONSTANT_4D; 1333 dw_ext1 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D; 1334 } 1335 1336 //One combination is a permutation of (0,0,0,2) based on c2 1337 xsv_ext2 = xsb; 1338 ysv_ext2 = ysb; 1339 zsv_ext2 = zsb; 1340 wsv_ext2 = wsb; 1341 dx_ext2 = dx0 - 2 * SQUISH_CONSTANT_4D; 1342 dy_ext2 = dy0 - 2 * SQUISH_CONSTANT_4D; 1343 dz_ext2 = dz0 - 2 * SQUISH_CONSTANT_4D; 1344 dw_ext2 = dw0 - 2 * SQUISH_CONSTANT_4D; 1345 if ((c2 & 0x01) != 0) { 1346 xsv_ext2 += 2; 1347 dx_ext2 -= 2; 1348 } else if ((c2 & 0x02) != 0) { 1349 ysv_ext2 += 2; 1350 dy_ext2 -= 2; 1351 } else if ((c2 & 0x04) != 0) { 1352 zsv_ext2 += 2; 1353 dz_ext2 -= 2; 1354 } else { 1355 wsv_ext2 += 2; 1356 dw_ext2 -= 2; 1357 } 1358 1359 } else { //Both closest points on the smaller side 1360 //One of the two extra points is (0,0,0,0) 1361 xsv_ext2 = xsb; 1362 ysv_ext2 = ysb; 1363 zsv_ext2 = zsb; 1364 wsv_ext2 = wsb; 1365 dx_ext2 = dx0; 1366 dy_ext2 = dy0; 1367 dz_ext2 = dz0; 1368 dw_ext2 = dw0; 1369 1370 //Other two points are based on the omitted axes. 1371 byte c = cast(byte)(aPoint | bPoint); 1372 1373 if ((c & 0x01) == 0) { 1374 xsv_ext0 = xsb - 1; 1375 xsv_ext1 = xsb; 1376 dx_ext0 = dx0 + 1 - SQUISH_CONSTANT_4D; 1377 dx_ext1 = dx0 - SQUISH_CONSTANT_4D; 1378 } else { 1379 xsv_ext0 = xsv_ext1 = xsb + 1; 1380 dx_ext0 = dx_ext1 = dx0 - 1 - SQUISH_CONSTANT_4D; 1381 } 1382 1383 if ((c & 0x02) == 0) { 1384 ysv_ext0 = ysv_ext1 = ysb; 1385 dy_ext0 = dy_ext1 = dy0 - SQUISH_CONSTANT_4D; 1386 if ((c & 0x01) == 0x01) 1387 { 1388 ysv_ext0 -= 1; 1389 dy_ext0 += 1; 1390 } else { 1391 ysv_ext1 -= 1; 1392 dy_ext1 += 1; 1393 } 1394 } else { 1395 ysv_ext0 = ysv_ext1 = ysb + 1; 1396 dy_ext0 = dy_ext1 = dy0 - 1 - SQUISH_CONSTANT_4D; 1397 } 1398 1399 if ((c & 0x04) == 0) { 1400 zsv_ext0 = zsv_ext1 = zsb; 1401 dz_ext0 = dz_ext1 = dz0 - SQUISH_CONSTANT_4D; 1402 if ((c & 0x03) == 0x03) 1403 { 1404 zsv_ext0 -= 1; 1405 dz_ext0 += 1; 1406 } else { 1407 zsv_ext1 -= 1; 1408 dz_ext1 += 1; 1409 } 1410 } else { 1411 zsv_ext0 = zsv_ext1 = zsb + 1; 1412 dz_ext0 = dz_ext1 = dz0 - 1 - SQUISH_CONSTANT_4D; 1413 } 1414 1415 if ((c & 0x08) == 0) 1416 { 1417 wsv_ext0 = wsb; 1418 wsv_ext1 = wsb - 1; 1419 dw_ext0 = dw0 - SQUISH_CONSTANT_4D; 1420 dw_ext1 = dw0 + 1 - SQUISH_CONSTANT_4D; 1421 } else { 1422 wsv_ext0 = wsv_ext1 = wsb + 1; 1423 dw_ext0 = dw_ext1 = dw0 - 1 - SQUISH_CONSTANT_4D; 1424 } 1425 1426 } 1427 } else { //One point on each "side" 1428 byte c1, c2; 1429 if (aIsBiggerSide) { 1430 c1 = aPoint; 1431 c2 = bPoint; 1432 } else { 1433 c1 = bPoint; 1434 c2 = aPoint; 1435 } 1436 1437 //Two contributions are the bigger-sided point with each 0 replaced with -1. 1438 if ((c1 & 0x01) == 0) { 1439 xsv_ext0 = xsb - 1; 1440 xsv_ext1 = xsb; 1441 dx_ext0 = dx0 + 1 - SQUISH_CONSTANT_4D; 1442 dx_ext1 = dx0 - SQUISH_CONSTANT_4D; 1443 } else { 1444 xsv_ext0 = xsv_ext1 = xsb + 1; 1445 dx_ext0 = dx_ext1 = dx0 - 1 - SQUISH_CONSTANT_4D; 1446 } 1447 1448 if ((c1 & 0x02) == 0) { 1449 ysv_ext0 = ysv_ext1 = ysb; 1450 dy_ext0 = dy_ext1 = dy0 - SQUISH_CONSTANT_4D; 1451 if ((c1 & 0x01) == 0x01) { 1452 ysv_ext0 -= 1; 1453 dy_ext0 += 1; 1454 } else { 1455 ysv_ext1 -= 1; 1456 dy_ext1 += 1; 1457 } 1458 } else { 1459 ysv_ext0 = ysv_ext1 = ysb + 1; 1460 dy_ext0 = dy_ext1 = dy0 - 1 - SQUISH_CONSTANT_4D; 1461 } 1462 1463 if ((c1 & 0x04) == 0) { 1464 zsv_ext0 = zsv_ext1 = zsb; 1465 dz_ext0 = dz_ext1 = dz0 - SQUISH_CONSTANT_4D; 1466 if ((c1 & 0x03) == 0x03) { 1467 zsv_ext0 -= 1; 1468 dz_ext0 += 1; 1469 } else { 1470 zsv_ext1 -= 1; 1471 dz_ext1 += 1; 1472 } 1473 } else { 1474 zsv_ext0 = zsv_ext1 = zsb + 1; 1475 dz_ext0 = dz_ext1 = dz0 - 1 - SQUISH_CONSTANT_4D; 1476 } 1477 1478 if ((c1 & 0x08) == 0) { 1479 wsv_ext0 = wsb; 1480 wsv_ext1 = wsb - 1; 1481 dw_ext0 = dw0 - SQUISH_CONSTANT_4D; 1482 dw_ext1 = dw0 + 1 - SQUISH_CONSTANT_4D; 1483 } else { 1484 wsv_ext0 = wsv_ext1 = wsb + 1; 1485 dw_ext0 = dw_ext1 = dw0 - 1 - SQUISH_CONSTANT_4D; 1486 } 1487 1488 //One contribution is a permutation of (0,0,0,2) based on the smaller-sided point 1489 xsv_ext2 = xsb; 1490 ysv_ext2 = ysb; 1491 zsv_ext2 = zsb; 1492 wsv_ext2 = wsb; 1493 dx_ext2 = dx0 - 2 * SQUISH_CONSTANT_4D; 1494 dy_ext2 = dy0 - 2 * SQUISH_CONSTANT_4D; 1495 dz_ext2 = dz0 - 2 * SQUISH_CONSTANT_4D; 1496 dw_ext2 = dw0 - 2 * SQUISH_CONSTANT_4D; 1497 if ((c2 & 0x01) != 0) { 1498 xsv_ext2 += 2; 1499 dx_ext2 -= 2; 1500 } else if ((c2 & 0x02) != 0) { 1501 ysv_ext2 += 2; 1502 dy_ext2 -= 2; 1503 } else if ((c2 & 0x04) != 0) { 1504 zsv_ext2 += 2; 1505 dz_ext2 -= 2; 1506 } else { 1507 wsv_ext2 += 2; 1508 dw_ext2 -= 2; 1509 } 1510 } 1511 1512 //Contribution (1,0,0,0) 1513 T dx1 = dx0 - 1 - SQUISH_CONSTANT_4D; 1514 T dy1 = dy0 - 0 - SQUISH_CONSTANT_4D; 1515 T dz1 = dz0 - 0 - SQUISH_CONSTANT_4D; 1516 T dw1 = dw0 - 0 - SQUISH_CONSTANT_4D; 1517 T attn1 = 2 - dx1 * dx1 - dy1 * dy1 - dz1 * dz1 - dw1 * dw1; 1518 if (attn1 > 0) { 1519 attn1 *= attn1; 1520 value += attn1 * attn1 * extrapolate(xsb + 1, ysb + 0, zsb + 0, wsb + 0, dx1, dy1, dz1, dw1); 1521 } 1522 1523 //Contribution (0,1,0,0) 1524 T dx2 = dx0 - 0 - SQUISH_CONSTANT_4D; 1525 T dy2 = dy0 - 1 - SQUISH_CONSTANT_4D; 1526 T dz2 = dz1; 1527 T dw2 = dw1; 1528 T attn2 = 2 - dx2 * dx2 - dy2 * dy2 - dz2 * dz2 - dw2 * dw2; 1529 if (attn2 > 0) { 1530 attn2 *= attn2; 1531 value += attn2 * attn2 * extrapolate(xsb + 0, ysb + 1, zsb + 0, wsb + 0, dx2, dy2, dz2, dw2); 1532 } 1533 1534 //Contribution (0,0,1,0) 1535 T dx3 = dx2; 1536 T dy3 = dy1; 1537 T dz3 = dz0 - 1 - SQUISH_CONSTANT_4D; 1538 T dw3 = dw1; 1539 T attn3 = 2 - dx3 * dx3 - dy3 * dy3 - dz3 * dz3 - dw3 * dw3; 1540 if (attn3 > 0) { 1541 attn3 *= attn3; 1542 value += attn3 * attn3 * extrapolate(xsb + 0, ysb + 0, zsb + 1, wsb + 0, dx3, dy3, dz3, dw3); 1543 } 1544 1545 //Contribution (0,0,0,1) 1546 T dx4 = dx2; 1547 T dy4 = dy1; 1548 T dz4 = dz1; 1549 T dw4 = dw0 - 1 - SQUISH_CONSTANT_4D; 1550 T attn4 = 2 - dx4 * dx4 - dy4 * dy4 - dz4 * dz4 - dw4 * dw4; 1551 if (attn4 > 0) { 1552 attn4 *= attn4; 1553 value += attn4 * attn4 * extrapolate(xsb + 0, ysb + 0, zsb + 0, wsb + 1, dx4, dy4, dz4, dw4); 1554 } 1555 1556 //Contribution (1,1,0,0) 1557 T dx5 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D; 1558 T dy5 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D; 1559 T dz5 = dz0 - 0 - 2 * SQUISH_CONSTANT_4D; 1560 T dw5 = dw0 - 0 - 2 * SQUISH_CONSTANT_4D; 1561 T attn5 = 2 - dx5 * dx5 - dy5 * dy5 - dz5 * dz5 - dw5 * dw5; 1562 if (attn5 > 0) { 1563 attn5 *= attn5; 1564 value += attn5 * attn5 * extrapolate(xsb + 1, ysb + 1, zsb + 0, wsb + 0, dx5, dy5, dz5, dw5); 1565 } 1566 1567 //Contribution (1,0,1,0) 1568 T dx6 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D; 1569 T dy6 = dy0 - 0 - 2 * SQUISH_CONSTANT_4D; 1570 T dz6 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D; 1571 T dw6 = dw0 - 0 - 2 * SQUISH_CONSTANT_4D; 1572 T attn6 = 2 - dx6 * dx6 - dy6 * dy6 - dz6 * dz6 - dw6 * dw6; 1573 if (attn6 > 0) { 1574 attn6 *= attn6; 1575 value += attn6 * attn6 * extrapolate(xsb + 1, ysb + 0, zsb + 1, wsb + 0, dx6, dy6, dz6, dw6); 1576 } 1577 1578 //Contribution (1,0,0,1) 1579 T dx7 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D; 1580 T dy7 = dy0 - 0 - 2 * SQUISH_CONSTANT_4D; 1581 T dz7 = dz0 - 0 - 2 * SQUISH_CONSTANT_4D; 1582 T dw7 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D; 1583 T attn7 = 2 - dx7 * dx7 - dy7 * dy7 - dz7 * dz7 - dw7 * dw7; 1584 if (attn7 > 0) { 1585 attn7 *= attn7; 1586 value += attn7 * attn7 * extrapolate(xsb + 1, ysb + 0, zsb + 0, wsb + 1, dx7, dy7, dz7, dw7); 1587 } 1588 1589 //Contribution (0,1,1,0) 1590 T dx8 = dx0 - 0 - 2 * SQUISH_CONSTANT_4D; 1591 T dy8 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D; 1592 T dz8 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D; 1593 T dw8 = dw0 - 0 - 2 * SQUISH_CONSTANT_4D; 1594 T attn8 = 2 - dx8 * dx8 - dy8 * dy8 - dz8 * dz8 - dw8 * dw8; 1595 if (attn8 > 0) { 1596 attn8 *= attn8; 1597 value += attn8 * attn8 * extrapolate(xsb + 0, ysb + 1, zsb + 1, wsb + 0, dx8, dy8, dz8, dw8); 1598 } 1599 1600 //Contribution (0,1,0,1) 1601 T dx9 = dx0 - 0 - 2 * SQUISH_CONSTANT_4D; 1602 T dy9 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D; 1603 T dz9 = dz0 - 0 - 2 * SQUISH_CONSTANT_4D; 1604 T dw9 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D; 1605 T attn9 = 2 - dx9 * dx9 - dy9 * dy9 - dz9 * dz9 - dw9 * dw9; 1606 if (attn9 > 0) { 1607 attn9 *= attn9; 1608 value += attn9 * attn9 * extrapolate(xsb + 0, ysb + 1, zsb + 0, wsb + 1, dx9, dy9, dz9, dw9); 1609 } 1610 1611 //Contribution (0,0,1,1) 1612 T dx10 = dx0 - 0 - 2 * SQUISH_CONSTANT_4D; 1613 T dy10 = dy0 - 0 - 2 * SQUISH_CONSTANT_4D; 1614 T dz10 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D; 1615 T dw10 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D; 1616 T attn10 = 2 - dx10 * dx10 - dy10 * dy10 - dz10 * dz10 - dw10 * dw10; 1617 if (attn10 > 0) { 1618 attn10 *= attn10; 1619 value += attn10 * attn10 * extrapolate(xsb + 0, ysb + 0, zsb + 1, wsb + 1, dx10, dy10, dz10, dw10); 1620 } 1621 } else { //We're inside the second dispentachoron (Rectified 4-Simplex) 1622 T aScore; 1623 byte aPoint; 1624 bool aIsBiggerSide = true; 1625 T bScore; 1626 byte bPoint; 1627 bool bIsBiggerSide = true; 1628 1629 //Decide between (0,0,1,1) and (1,1,0,0) 1630 if (xins + yins < zins + wins) { 1631 aScore = xins + yins; 1632 aPoint = 0x0C; 1633 } else { 1634 aScore = zins + wins; 1635 aPoint = 0x03; 1636 } 1637 1638 //Decide between (0,1,0,1) and (1,0,1,0) 1639 if (xins + zins < yins + wins) { 1640 bScore = xins + zins; 1641 bPoint = 0x0A; 1642 } else { 1643 bScore = yins + wins; 1644 bPoint = 0x05; 1645 } 1646 1647 //Closer between (0,1,1,0) and (1,0,0,1) will replace the further of a and b, if closer. 1648 if (xins + wins < yins + zins) { 1649 T score = xins + wins; 1650 if (aScore <= bScore && score < bScore) { 1651 bScore = score; 1652 bPoint = 0x06; 1653 } else if (aScore > bScore && score < aScore) { 1654 aScore = score; 1655 aPoint = 0x06; 1656 } 1657 } else { 1658 T score = yins + zins; 1659 if (aScore <= bScore && score < bScore) { 1660 bScore = score; 1661 bPoint = 0x09; 1662 } else if (aScore > bScore && score < aScore) { 1663 aScore = score; 1664 aPoint = 0x09; 1665 } 1666 } 1667 1668 //Decide if (0,1,1,1) is closer. 1669 T p1 = 3 - inSum + xins; 1670 if (aScore <= bScore && p1 < bScore) { 1671 bScore = p1; 1672 bPoint = 0x0E; 1673 bIsBiggerSide = false; 1674 } else if (aScore > bScore && p1 < aScore) { 1675 aScore = p1; 1676 aPoint = 0x0E; 1677 aIsBiggerSide = false; 1678 } 1679 1680 //Decide if (1,0,1,1) is closer. 1681 T p2 = 3 - inSum + yins; 1682 if (aScore <= bScore && p2 < bScore) { 1683 bScore = p2; 1684 bPoint = 0x0D; 1685 bIsBiggerSide = false; 1686 } else if (aScore > bScore && p2 < aScore) { 1687 aScore = p2; 1688 aPoint = 0x0D; 1689 aIsBiggerSide = false; 1690 } 1691 1692 //Decide if (1,1,0,1) is closer. 1693 T p3 = 3 - inSum + zins; 1694 if (aScore <= bScore && p3 < bScore) { 1695 bScore = p3; 1696 bPoint = 0x0B; 1697 bIsBiggerSide = false; 1698 } else if (aScore > bScore && p3 < aScore) { 1699 aScore = p3; 1700 aPoint = 0x0B; 1701 aIsBiggerSide = false; 1702 } 1703 1704 //Decide if (1,1,1,0) is closer. 1705 T p4 = 3 - inSum + wins; 1706 if (aScore <= bScore && p4 < bScore) { 1707 bScore = p4; 1708 bPoint = 0x07; 1709 bIsBiggerSide = false; 1710 } else if (aScore > bScore && p4 < aScore) { 1711 aScore = p4; 1712 aPoint = 0x07; 1713 aIsBiggerSide = false; 1714 } 1715 1716 //Where each of the two closest points are determines how the extra three vertices are calculated. 1717 if (aIsBiggerSide == bIsBiggerSide) { 1718 if (aIsBiggerSide) { //Both closest points on the bigger side 1719 byte c1 = cast(byte)(aPoint & bPoint); 1720 byte c2 = cast(byte)(aPoint | bPoint); 1721 1722 //Two contributions are permutations of (0,0,0,1) and (0,0,0,2) based on c1 1723 xsv_ext0 = xsv_ext1 = xsb; 1724 ysv_ext0 = ysv_ext1 = ysb; 1725 zsv_ext0 = zsv_ext1 = zsb; 1726 wsv_ext0 = wsv_ext1 = wsb; 1727 dx_ext0 = dx0 - SQUISH_CONSTANT_4D; 1728 dy_ext0 = dy0 - SQUISH_CONSTANT_4D; 1729 dz_ext0 = dz0 - SQUISH_CONSTANT_4D; 1730 dw_ext0 = dw0 - SQUISH_CONSTANT_4D; 1731 dx_ext1 = dx0 - 2 * SQUISH_CONSTANT_4D; 1732 dy_ext1 = dy0 - 2 * SQUISH_CONSTANT_4D; 1733 dz_ext1 = dz0 - 2 * SQUISH_CONSTANT_4D; 1734 dw_ext1 = dw0 - 2 * SQUISH_CONSTANT_4D; 1735 if ((c1 & 0x01) != 0) { 1736 xsv_ext0 += 1; 1737 dx_ext0 -= 1; 1738 xsv_ext1 += 2; 1739 dx_ext1 -= 2; 1740 } else if ((c1 & 0x02) != 0) { 1741 ysv_ext0 += 1; 1742 dy_ext0 -= 1; 1743 ysv_ext1 += 2; 1744 dy_ext1 -= 2; 1745 } else if ((c1 & 0x04) != 0) { 1746 zsv_ext0 += 1; 1747 dz_ext0 -= 1; 1748 zsv_ext1 += 2; 1749 dz_ext1 -= 2; 1750 } else { 1751 wsv_ext0 += 1; 1752 dw_ext0 -= 1; 1753 wsv_ext1 += 2; 1754 dw_ext1 -= 2; 1755 } 1756 1757 //One contribution is a permutation of (1,1,1,-1) based on c2 1758 xsv_ext2 = xsb + 1; 1759 ysv_ext2 = ysb + 1; 1760 zsv_ext2 = zsb + 1; 1761 wsv_ext2 = wsb + 1; 1762 dx_ext2 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D; 1763 dy_ext2 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D; 1764 dz_ext2 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D; 1765 dw_ext2 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D; 1766 if ((c2 & 0x01) == 0) { 1767 xsv_ext2 -= 2; 1768 dx_ext2 += 2; 1769 } else if ((c2 & 0x02) == 0) { 1770 ysv_ext2 -= 2; 1771 dy_ext2 += 2; 1772 } else if ((c2 & 0x04) == 0) { 1773 zsv_ext2 -= 2; 1774 dz_ext2 += 2; 1775 } else { 1776 wsv_ext2 -= 2; 1777 dw_ext2 += 2; 1778 } 1779 } else { //Both closest points on the smaller side 1780 //One of the two extra points is (1,1,1,1) 1781 xsv_ext2 = xsb + 1; 1782 ysv_ext2 = ysb + 1; 1783 zsv_ext2 = zsb + 1; 1784 wsv_ext2 = wsb + 1; 1785 dx_ext2 = dx0 - 1 - 4 * SQUISH_CONSTANT_4D; 1786 dy_ext2 = dy0 - 1 - 4 * SQUISH_CONSTANT_4D; 1787 dz_ext2 = dz0 - 1 - 4 * SQUISH_CONSTANT_4D; 1788 dw_ext2 = dw0 - 1 - 4 * SQUISH_CONSTANT_4D; 1789 1790 //Other two points are based on the shared axes. 1791 byte c = cast(byte)(aPoint & bPoint); 1792 1793 if ((c & 0x01) != 0) { 1794 xsv_ext0 = xsb + 2; 1795 xsv_ext1 = xsb + 1; 1796 dx_ext0 = dx0 - 2 - 3 * SQUISH_CONSTANT_4D; 1797 dx_ext1 = dx0 - 1 - 3 * SQUISH_CONSTANT_4D; 1798 } else { 1799 xsv_ext0 = xsv_ext1 = xsb; 1800 dx_ext0 = dx_ext1 = dx0 - 3 * SQUISH_CONSTANT_4D; 1801 } 1802 1803 if ((c & 0x02) != 0) { 1804 ysv_ext0 = ysv_ext1 = ysb + 1; 1805 dy_ext0 = dy_ext1 = dy0 - 1 - 3 * SQUISH_CONSTANT_4D; 1806 if ((c & 0x01) == 0) 1807 { 1808 ysv_ext0 += 1; 1809 dy_ext0 -= 1; 1810 } else { 1811 ysv_ext1 += 1; 1812 dy_ext1 -= 1; 1813 } 1814 } else { 1815 ysv_ext0 = ysv_ext1 = ysb; 1816 dy_ext0 = dy_ext1 = dy0 - 3 * SQUISH_CONSTANT_4D; 1817 } 1818 1819 if ((c & 0x04) != 0) { 1820 zsv_ext0 = zsv_ext1 = zsb + 1; 1821 dz_ext0 = dz_ext1 = dz0 - 1 - 3 * SQUISH_CONSTANT_4D; 1822 if ((c & 0x03) == 0) 1823 { 1824 zsv_ext0 += 1; 1825 dz_ext0 -= 1; 1826 } else { 1827 zsv_ext1 += 1; 1828 dz_ext1 -= 1; 1829 } 1830 } else { 1831 zsv_ext0 = zsv_ext1 = zsb; 1832 dz_ext0 = dz_ext1 = dz0 - 3 * SQUISH_CONSTANT_4D; 1833 } 1834 1835 if ((c & 0x08) != 0) 1836 { 1837 wsv_ext0 = wsb + 1; 1838 wsv_ext1 = wsb + 2; 1839 dw_ext0 = dw0 - 1 - 3 * SQUISH_CONSTANT_4D; 1840 dw_ext1 = dw0 - 2 - 3 * SQUISH_CONSTANT_4D; 1841 } else { 1842 wsv_ext0 = wsv_ext1 = wsb; 1843 dw_ext0 = dw_ext1 = dw0 - 3 * SQUISH_CONSTANT_4D; 1844 } 1845 } 1846 } else { //One point on each "side" 1847 byte c1, c2; 1848 if (aIsBiggerSide) { 1849 c1 = aPoint; 1850 c2 = bPoint; 1851 } else { 1852 c1 = bPoint; 1853 c2 = aPoint; 1854 } 1855 1856 //Two contributions are the bigger-sided point with each 1 replaced with 2. 1857 if ((c1 & 0x01) != 0) { 1858 xsv_ext0 = xsb + 2; 1859 xsv_ext1 = xsb + 1; 1860 dx_ext0 = dx0 - 2 - 3 * SQUISH_CONSTANT_4D; 1861 dx_ext1 = dx0 - 1 - 3 * SQUISH_CONSTANT_4D; 1862 } else { 1863 xsv_ext0 = xsv_ext1 = xsb; 1864 dx_ext0 = dx_ext1 = dx0 - 3 * SQUISH_CONSTANT_4D; 1865 } 1866 1867 if ((c1 & 0x02) != 0) { 1868 ysv_ext0 = ysv_ext1 = ysb + 1; 1869 dy_ext0 = dy_ext1 = dy0 - 1 - 3 * SQUISH_CONSTANT_4D; 1870 if ((c1 & 0x01) == 0) { 1871 ysv_ext0 += 1; 1872 dy_ext0 -= 1; 1873 } else { 1874 ysv_ext1 += 1; 1875 dy_ext1 -= 1; 1876 } 1877 } else { 1878 ysv_ext0 = ysv_ext1 = ysb; 1879 dy_ext0 = dy_ext1 = dy0 - 3 * SQUISH_CONSTANT_4D; 1880 } 1881 1882 if ((c1 & 0x04) != 0) { 1883 zsv_ext0 = zsv_ext1 = zsb + 1; 1884 dz_ext0 = dz_ext1 = dz0 - 1 - 3 * SQUISH_CONSTANT_4D; 1885 if ((c1 & 0x03) == 0) { 1886 zsv_ext0 += 1; 1887 dz_ext0 -= 1; 1888 } else { 1889 zsv_ext1 += 1; 1890 dz_ext1 -= 1; 1891 } 1892 } else { 1893 zsv_ext0 = zsv_ext1 = zsb; 1894 dz_ext0 = dz_ext1 = dz0 - 3 * SQUISH_CONSTANT_4D; 1895 } 1896 1897 if ((c1 & 0x08) != 0) { 1898 wsv_ext0 = wsb + 1; 1899 wsv_ext1 = wsb + 2; 1900 dw_ext0 = dw0 - 1 - 3 * SQUISH_CONSTANT_4D; 1901 dw_ext1 = dw0 - 2 - 3 * SQUISH_CONSTANT_4D; 1902 } else { 1903 wsv_ext0 = wsv_ext1 = wsb; 1904 dw_ext0 = dw_ext1 = dw0 - 3 * SQUISH_CONSTANT_4D; 1905 } 1906 1907 //One contribution is a permutation of (1,1,1,-1) based on the smaller-sided point 1908 xsv_ext2 = xsb + 1; 1909 ysv_ext2 = ysb + 1; 1910 zsv_ext2 = zsb + 1; 1911 wsv_ext2 = wsb + 1; 1912 dx_ext2 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D; 1913 dy_ext2 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D; 1914 dz_ext2 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D; 1915 dw_ext2 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D; 1916 if ((c2 & 0x01) == 0) { 1917 xsv_ext2 -= 2; 1918 dx_ext2 += 2; 1919 } else if ((c2 & 0x02) == 0) { 1920 ysv_ext2 -= 2; 1921 dy_ext2 += 2; 1922 } else if ((c2 & 0x04) == 0) { 1923 zsv_ext2 -= 2; 1924 dz_ext2 += 2; 1925 } else { 1926 wsv_ext2 -= 2; 1927 dw_ext2 += 2; 1928 } 1929 } 1930 1931 //Contribution (1,1,1,0) 1932 T dx4 = dx0 - 1 - 3 * SQUISH_CONSTANT_4D; 1933 T dy4 = dy0 - 1 - 3 * SQUISH_CONSTANT_4D; 1934 T dz4 = dz0 - 1 - 3 * SQUISH_CONSTANT_4D; 1935 T dw4 = dw0 - 3 * SQUISH_CONSTANT_4D; 1936 T attn4 = 2 - dx4 * dx4 - dy4 * dy4 - dz4 * dz4 - dw4 * dw4; 1937 if (attn4 > 0) { 1938 attn4 *= attn4; 1939 value += attn4 * attn4 * extrapolate(xsb + 1, ysb + 1, zsb + 1, wsb + 0, dx4, dy4, dz4, dw4); 1940 } 1941 1942 //Contribution (1,1,0,1) 1943 T dx3 = dx4; 1944 T dy3 = dy4; 1945 T dz3 = dz0 - 3 * SQUISH_CONSTANT_4D; 1946 T dw3 = dw0 - 1 - 3 * SQUISH_CONSTANT_4D; 1947 T attn3 = 2 - dx3 * dx3 - dy3 * dy3 - dz3 * dz3 - dw3 * dw3; 1948 if (attn3 > 0) { 1949 attn3 *= attn3; 1950 value += attn3 * attn3 * extrapolate(xsb + 1, ysb + 1, zsb + 0, wsb + 1, dx3, dy3, dz3, dw3); 1951 } 1952 1953 //Contribution (1,0,1,1) 1954 T dx2 = dx4; 1955 T dy2 = dy0 - 3 * SQUISH_CONSTANT_4D; 1956 T dz2 = dz4; 1957 T dw2 = dw3; 1958 T attn2 = 2 - dx2 * dx2 - dy2 * dy2 - dz2 * dz2 - dw2 * dw2; 1959 if (attn2 > 0) { 1960 attn2 *= attn2; 1961 value += attn2 * attn2 * extrapolate(xsb + 1, ysb + 0, zsb + 1, wsb + 1, dx2, dy2, dz2, dw2); 1962 } 1963 1964 //Contribution (0,1,1,1) 1965 T dx1 = dx0 - 3 * SQUISH_CONSTANT_4D; 1966 T dz1 = dz4; 1967 T dy1 = dy4; 1968 T dw1 = dw3; 1969 T attn1 = 2 - dx1 * dx1 - dy1 * dy1 - dz1 * dz1 - dw1 * dw1; 1970 if (attn1 > 0) { 1971 attn1 *= attn1; 1972 value += attn1 * attn1 * extrapolate(xsb + 0, ysb + 1, zsb + 1, wsb + 1, dx1, dy1, dz1, dw1); 1973 } 1974 1975 //Contribution (1,1,0,0) 1976 T dx5 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D; 1977 T dy5 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D; 1978 T dz5 = dz0 - 0 - 2 * SQUISH_CONSTANT_4D; 1979 T dw5 = dw0 - 0 - 2 * SQUISH_CONSTANT_4D; 1980 T attn5 = 2 - dx5 * dx5 - dy5 * dy5 - dz5 * dz5 - dw5 * dw5; 1981 if (attn5 > 0) { 1982 attn5 *= attn5; 1983 value += attn5 * attn5 * extrapolate(xsb + 1, ysb + 1, zsb + 0, wsb + 0, dx5, dy5, dz5, dw5); 1984 } 1985 1986 //Contribution (1,0,1,0) 1987 T dx6 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D; 1988 T dy6 = dy0 - 0 - 2 * SQUISH_CONSTANT_4D; 1989 T dz6 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D; 1990 T dw6 = dw0 - 0 - 2 * SQUISH_CONSTANT_4D; 1991 T attn6 = 2 - dx6 * dx6 - dy6 * dy6 - dz6 * dz6 - dw6 * dw6; 1992 if (attn6 > 0) { 1993 attn6 *= attn6; 1994 value += attn6 * attn6 * extrapolate(xsb + 1, ysb + 0, zsb + 1, wsb + 0, dx6, dy6, dz6, dw6); 1995 } 1996 1997 //Contribution (1,0,0,1) 1998 T dx7 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D; 1999 T dy7 = dy0 - 0 - 2 * SQUISH_CONSTANT_4D; 2000 T dz7 = dz0 - 0 - 2 * SQUISH_CONSTANT_4D; 2001 T dw7 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D; 2002 T attn7 = 2 - dx7 * dx7 - dy7 * dy7 - dz7 * dz7 - dw7 * dw7; 2003 if (attn7 > 0) { 2004 attn7 *= attn7; 2005 value += attn7 * attn7 * extrapolate(xsb + 1, ysb + 0, zsb + 0, wsb + 1, dx7, dy7, dz7, dw7); 2006 } 2007 2008 //Contribution (0,1,1,0) 2009 T dx8 = dx0 - 0 - 2 * SQUISH_CONSTANT_4D; 2010 T dy8 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D; 2011 T dz8 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D; 2012 T dw8 = dw0 - 0 - 2 * SQUISH_CONSTANT_4D; 2013 T attn8 = 2 - dx8 * dx8 - dy8 * dy8 - dz8 * dz8 - dw8 * dw8; 2014 if (attn8 > 0) { 2015 attn8 *= attn8; 2016 value += attn8 * attn8 * extrapolate(xsb + 0, ysb + 1, zsb + 1, wsb + 0, dx8, dy8, dz8, dw8); 2017 } 2018 2019 //Contribution (0,1,0,1) 2020 T dx9 = dx0 - 0 - 2 * SQUISH_CONSTANT_4D; 2021 T dy9 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D; 2022 T dz9 = dz0 - 0 - 2 * SQUISH_CONSTANT_4D; 2023 T dw9 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D; 2024 T attn9 = 2 - dx9 * dx9 - dy9 * dy9 - dz9 * dz9 - dw9 * dw9; 2025 if (attn9 > 0) { 2026 attn9 *= attn9; 2027 value += attn9 * attn9 * extrapolate(xsb + 0, ysb + 1, zsb + 0, wsb + 1, dx9, dy9, dz9, dw9); 2028 } 2029 2030 //Contribution (0,0,1,1) 2031 T dx10 = dx0 - 0 - 2 * SQUISH_CONSTANT_4D; 2032 T dy10 = dy0 - 0 - 2 * SQUISH_CONSTANT_4D; 2033 T dz10 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D; 2034 T dw10 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D; 2035 T attn10 = 2 - dx10 * dx10 - dy10 * dy10 - dz10 * dz10 - dw10 * dw10; 2036 if (attn10 > 0) { 2037 attn10 *= attn10; 2038 value += attn10 * attn10 * extrapolate(xsb + 0, ysb + 0, zsb + 1, wsb + 1, dx10, dy10, dz10, dw10); 2039 } 2040 } 2041 2042 //First extra vertex 2043 T attn_ext0 = 2 - dx_ext0 * dx_ext0 - dy_ext0 * dy_ext0 - dz_ext0 * dz_ext0 - dw_ext0 * dw_ext0; 2044 if (attn_ext0 > 0) 2045 { 2046 attn_ext0 *= attn_ext0; 2047 value += attn_ext0 * attn_ext0 * extrapolate(xsv_ext0, ysv_ext0, zsv_ext0, wsv_ext0, dx_ext0, dy_ext0, dz_ext0, dw_ext0); 2048 } 2049 2050 //Second extra vertex 2051 T attn_ext1 = 2 - dx_ext1 * dx_ext1 - dy_ext1 * dy_ext1 - dz_ext1 * dz_ext1 - dw_ext1 * dw_ext1; 2052 if (attn_ext1 > 0) 2053 { 2054 attn_ext1 *= attn_ext1; 2055 value += attn_ext1 * attn_ext1 * extrapolate(xsv_ext1, ysv_ext1, zsv_ext1, wsv_ext1, dx_ext1, dy_ext1, dz_ext1, dw_ext1); 2056 } 2057 2058 //Third extra vertex 2059 T attn_ext2 = 2 - dx_ext2 * dx_ext2 - dy_ext2 * dy_ext2 - dz_ext2 * dz_ext2 - dw_ext2 * dw_ext2; 2060 if (attn_ext2 > 0) 2061 { 2062 attn_ext2 *= attn_ext2; 2063 value += attn_ext2 * attn_ext2 * extrapolate(xsv_ext2, ysv_ext2, zsv_ext2, wsv_ext2, dx_ext2, dy_ext2, dz_ext2, dw_ext2); 2064 } 2065 2066 return value / NORM_CONSTANT_4D; 2067 } 2068 2069 private T extrapolate(int xsb, int ysb, T dx, T dy) 2070 { 2071 int index = perm[(perm[xsb & 0xFF] + ysb) & 0xFF] & 0x0E; 2072 return gradients2D[index] * dx 2073 + gradients2D[index + 1] * dy; 2074 } 2075 2076 private T extrapolate(int xsb, int ysb, int zsb, T dx, T dy, T dz) 2077 { 2078 int index = permGradIndex3D[(perm[(perm[xsb & 0xFF] + ysb) & 0xFF] + zsb) & 0xFF]; 2079 return gradients3D[index] * dx 2080 + gradients3D[index + 1] * dy 2081 + gradients3D[index + 2] * dz; 2082 } 2083 2084 private T extrapolate(int xsb, int ysb, int zsb, int wsb, T dx, T dy, T dz, T dw) 2085 { 2086 int index = perm[(perm[(perm[(perm[xsb & 0xFF] + ysb) & 0xFF] + zsb) & 0xFF] + wsb) & 0xFF] & 0xFC; 2087 return gradients4D[index] * dx 2088 + gradients4D[index + 1] * dy 2089 + gradients4D[index + 2] * dz 2090 + gradients4D[index + 3] * dw; 2091 } 2092 2093 private static int fastFloor(T x) { 2094 int xi = cast(int)x; 2095 return x < xi ? xi - 1 : xi; 2096 } 2097 2098 //Gradients for 2D. They approximate the directions to the 2099 //vertices of an octagon from the center. 2100 private static immutable byte[] gradients2D = [ 2101 5, 2, 2, 5, 2102 -5, 2, -2, 5, 2103 5, -2, 2, -5, 2104 -5, -2, -2, -5, 2105 ]; 2106 2107 //Gradients for 3D. They approximate the directions to the 2108 //vertices of a rhombicuboctahedron from the center, skewed so 2109 //that the triangular and square facets can be inscribed inside 2110 //circles of the same radius. 2111 private static immutable byte[] gradients3D = [ 2112 -11, 4, 4, -4, 11, 4, -4, 4, 11, 2113 11, 4, 4, 4, 11, 4, 4, 4, 11, 2114 -11, -4, 4, -4, -11, 4, -4, -4, 11, 2115 11, -4, 4, 4, -11, 4, 4, -4, 11, 2116 -11, 4, -4, -4, 11, -4, -4, 4, -11, 2117 11, 4, -4, 4, 11, -4, 4, 4, -11, 2118 -11, -4, -4, -4, -11, -4, -4, -4, -11, 2119 11, -4, -4, 4, -11, -4, 4, -4, -11, 2120 ]; 2121 2122 //Gradients for 4D. They approximate the directions to the 2123 //vertices of a disprismatotesseractihexadecachoron from the center, 2124 //skewed so that the tetrahedral and cubic facets can be inscribed inside 2125 //spheres of the same radius. 2126 private static immutable byte[] gradients4D = [ 2127 3, 1, 1, 1, 1, 3, 1, 1, 1, 1, 3, 1, 1, 1, 1, 3, 2128 -3, 1, 1, 1, -1, 3, 1, 1, -1, 1, 3, 1, -1, 1, 1, 3, 2129 3, -1, 1, 1, 1, -3, 1, 1, 1, -1, 3, 1, 1, -1, 1, 3, 2130 -3, -1, 1, 1, -1, -3, 1, 1, -1, -1, 3, 1, -1, -1, 1, 3, 2131 3, 1, -1, 1, 1, 3, -1, 1, 1, 1, -3, 1, 1, 1, -1, 3, 2132 -3, 1, -1, 1, -1, 3, -1, 1, -1, 1, -3, 1, -1, 1, -1, 3, 2133 3, -1, -1, 1, 1, -3, -1, 1, 1, -1, -3, 1, 1, -1, -1, 3, 2134 -3, -1, -1, 1, -1, -3, -1, 1, -1, -1, -3, 1, -1, -1, -1, 3, 2135 3, 1, 1, -1, 1, 3, 1, -1, 1, 1, 3, -1, 1, 1, 1, -3, 2136 -3, 1, 1, -1, -1, 3, 1, -1, -1, 1, 3, -1, -1, 1, 1, -3, 2137 3, -1, 1, -1, 1, -3, 1, -1, 1, -1, 3, -1, 1, -1, 1, -3, 2138 -3, -1, 1, -1, -1, -3, 1, -1, -1, -1, 3, -1, -1, -1, 1, -3, 2139 3, 1, -1, -1, 1, 3, -1, -1, 1, 1, -3, -1, 1, 1, -1, -3, 2140 -3, 1, -1, -1, -1, 3, -1, -1, -1, 1, -3, -1, -1, 1, -1, -3, 2141 3, -1, -1, -1, 1, -3, -1, -1, 1, -1, -3, -1, 1, -1, -1, -3, 2142 -3, -1, -1, -1, -1, -3, -1, -1, -1, -1, -3, -1, -1, -1, -1, -3, 2143 ]; 2144 }